This was largely ignored. Throughout a significant part of his life, Stalin lived outside Georgia, did not use his surname Dzhugashvili, did not use the Georgian language every day and wrote in Georgian only to his mother. It is also known that Stalin's children, who lived permanently in Moscow and the Moscow region, were cut off from the people to which their father belonged.

Stalin seemed to his children as Russian as their mother was and as they were themselves. Svetlana recalled how Vasily once told her: "You know, our father used to be Georgian." Svetlana recalled: "I was 6 years old, and I did not know what it meant to be a Georgian. Then eleven-year-old Vasily explained to me: They wear Circassian coats and cut everyone with daggers." Since Stalin did not wear a Circassian coat and the children did not see him cut people with a dagger, Vasily and Svetlana decided that their father had already ceased to be Georgian.

Source: Ada Petrova, Mikhail Leshchinsky, Stalin's daughter. Last interview (compilation), 2011

Since your question was already answered but you might be interested in further context I'll provide some. The "Georgian Affair," gives us some idea about Stalin's attitude towards his home country, as well as demonstrating his position in the consequential debate around the extent and nature of national self-determination within the Soviet Union.

In 1922 Lenin was disabled from sickness, his death was impending. The Politburo was aware that his death would have far reaching implications. The exact dimensions of Lenin's position as a leader are still debated. They generally range somewhere between two understandings: At one end there are those who see Lenin as a dictatorial leader whose brutal decrees may not have matched Stalin's in scale, but nonetheless laid the groundwork for Stalin's regime. Max Eastman and Stephen Kotkin are among those supporting this theory. At the other end, Lenin is understood as a leader whose de facto authority over the Central Committee was never intended or expected by Lenin or any others to be inherited His role in early Soviet politics was defined more by the tremendous prestige he wielded as the foremost of the Old Bolsheviks: he had the credentials of a lifelong revolutionary, he was an accomplished and influential theorist within the broader European socialist milieus, and as a leader had a talent for energetic delegation and timely interventions. In this view, whatever might be said about the dictatorship of the party over the country and their restrictions on factions and political plurality, the party and state apparatus themselves were never intended or expected to be free from internal debate and disagreement or concentrated under the power of any single figure. Moshe Lewin defends this interpretation. In Jerry F. Fough's "How the Soviet Union is Governed", Fough presents both interpretations, generally giving more credence to the latter but noting that even understood as a usurper of a relatively democratic intra-party politics, Stalin drew heavily on the precedents of anti-factionalism and the unrestricted political suppression developed during the Civil War to shore up whatever gains he made while accumulating power. Even historians like Kotkin, who condemn Lenin far more harshly and see him as an understandable predecessor to Stalin, are in agreement that the sickness and death of Lenin did not usher in a free-for-all power grab among self-professed successors: most expected that after Lenin's death collective power distributed among various offices would constitute the party's leadership. Kotkin writes in Chapter 10 of his Stalin biography:

"Lenin was undisputed leader (vozhd’) and no one imagined he might become incapacitated. When that suddenly happened, most everyone assumed collective leadership would prevail: even if other top Bolsheviks believed in their heart of hearts they might be Lenin’s equal, they understood no one else would perceive them as such."

Besides there being no expectation of a single man filling Lenin's shoes, let alone far exceeding Lenin's degree of authority, Stalin himself was not an especially prestigious or respected member of the Politburo. Sukhanov reported that Stalin "produced-and not only on me-the impression of a gray blur, looming up now and then dimly and not leaving any trace. There is really nothing more to be said about him." Stalin's office in the Politburo, General-Secretary, was not an especially remarkable position and consisted largely of organizing meetings and fulfilling the administrative side of party membership. The role was really that of a secretary concerned with the general functions of the party and the state apparatus. Fough describes him as basically Lenin's equivalent to a White House Chief-of-Staff. This later gave him outsized power in expelling party members, as well as an enormous amounts of contacts he had corresponded with as part of his job as secretary, all of which allowed for his shrewd tactics of joining and abandoning cliques, expelling their respective political opponents, and pivoting to do the same to his own former conspirators with a new set of provisional allies until he had cemented his position. In 1921-1923, he remained largely unremarkable, but his ambitions were clear in his concerted efforts to cozy up to a dying Lenin and project an exaggerated closeness between the two to curry respectability and legitimacy within the Politburo and the party in general. At this point Lenin's contact with the outside world was limited by the recovery protocol he doctors had demanded, so Lenin largely enjoyed these visits and appreciated getting updates on the unfolding situation, as well as sharing his thoughts with Stalin. This of course means that Lenin's interpretation of events was to some extent mediated through Stalin (though he also of course received updates in other forms, these were limited to try and keep him relaxed for recovery), and reports of Lenin's thoughts and positions was to some extent mediated through Stalin. This element should not be exaggerated however, and it is more significant that Stalin was inculcating the narrative of a close personal friendship to Stalin, when by all accounts Lenin simply respected him in a professional sense.

Where this becomes relevant to your question about Georgia is that during this uncertain period, with Lenin's health declining and highly consequential decisions being made as to the form the party would take, Lenin and Stalin had a fierce disagreement over the matter of Georgia's incorporation into the USSR. Stalin had a history of overstepping on the matter of Georgia. In 1921, Georgia was having its own socialist unrest, in the form of radical peasant revolts and the struggles of a moderate democratically elected socialist government to handle wars with Armenia and the Ottomans. Trotsky, leader of the Red Army, did not approve of intervention in Georgia. Lenin expressed skepticism but approved. Stalin organized an invasion of the country alongside Sergo Ordzhonikidze (another Russian Bolshevik of Georgian origin), installing the Georgian Bolsheviks in power and leading to the creation of the Georgian SSR. But the status of the Republics had not yet been well-delineated. During the Civil War there had been significant strongarming and measures taken to ensure de facto Soviet rule and limiting the national autonomy of Soviet aligned Republics, but it was not taken for granted that this would continue or that the Republics would be mere satellites. For his part, Stalin had long opposed national autonomy, and his role in the creation of the Georgian SSR allowed him to deny the Republic the right to form its own Red Army, and forced the Georgian trade unions and various socialist groups to subordinate themselves to the Bolshevik leadership he and his companions had installed. He gave a speech about the necessity of rooting out Georgian nationalism, which was booed by the crowd and silently received with disdain from the Georgian Bolsheviks Stalin's own expedition had installed. In response, Stalin had the leader of the Georgian Bolsheviks replaced with his own choice of leader, and saw that he went about suppressing any national sentiments. He would eventually come to harsh disagreement with the very man he had installed, Mdivani, due to his resistance to Stalin's proposition to unite three Caucasian countries — Georgia, Armenia, and Azerbaijan — into a single Transcaucasian Republic. The leadership of Georgia, already unsure about joining as a Soviet Republic when the status of their autonomy within it was unclear, were unsurprisingly against the idea of their conglomeration. The situation deteriorated, Stalin accused the Georgian Bolsheviks of being nationalist reactionaries, and Mdivani and his supporters complained to Lenin about what they considered Russian chauvinism. Lenin initially upheld Stalin's position, but after a later disagreement led to Ordzhonikidze physically attacking some of Mdivani's supporters, Lenin dispatched a team to investigate what was happening.