My only experience with Ba'athism was knowing that it was Saddam's "ideology" and the Ba'ath party effectively served a role in the Iraqi state much like the Nazi party did within Germany, where membership in the party conferred access and was used for the leader as a buffer against potential internal threats in the government. I was surprised to learn that Assad's family is a Ba'ath party thing given how tense Iraq and Syria have been for ages. You'd think it would be more friendly, like how Hitler and Mussolini were friendly over shared ideological principles as well as mutual enemies. Despite that, my understanding is that Syria has generally remained out of much of the conflicts right up until the Arab Spring and was never particularly friendly or an ally to Saddam.
I've also seen some of the more wacky types of socialists ("tankies") defending Ba'ath regimes as "socialist" which is pretty strange to me given that in any incarnation that I've actually seen them, they far more closely resemble a sort of muted fascism or vague nationalism than any sort of Marxist ideology.
I've read that at one point it was nominally a socialist or communist ideology with a lot of "true believers," and I'm curious about how that was true, what changed, what the Ba'ath party even is if it has any ideology today and so on.
Ba'athism is a mix of 'moderate' socialism, authoritarianism, and Arab nationalism, with elements of Islamic socialism and pan-Arabism. Although it drank from the same well as Fascism by being partially inspired by Nietzche, it is significantly more inspired by socialist thought, such as that of Marx, Lenin, and Blanqui.
Basically, Ba'athism was a "progressivized" adaption of conservative Arab nationalism that looks to create an Arab cultural renaissance (Ba'ath literally translates to renaissance) and a single, pan-Arab state. The founder of Ba'athism, Michel Aflaq, saw that the Arab world had significantly declined since the Islamic Golden Age, and concluded that reactionary politics, foreign imperialism, intellectual backwardness, religious fundamentalism, and regional petty squabbles were the fault. He resolved that things couldn't be fixed by reform, so a vanguard of enlightened authoritarian progressives had to take over by hook or by crook, and restructure society.
In Marxist thought, feudalism naturally led to capitalism, which would in turn lead to socialism, which would in turn lead to communism. Aflaq partially disagreed. He thought that Middle Eastern feudalism and stratification was so intense, that liberal capitalist democracy wouldn't be able to breach and, and thus concluded that the Arab people should 'skip over' capitalism and go straight to socialism, which could economically bring about the Ba'ath (renaissance) much faster than capitalism could, and would also result in the end of economic dominance of any one group over another (except for the vanguard, which had to maintain control to look after the people, you see). In practice, Ba'athist countries such as Iraq and Syria nationalized major industry, such as oil, but allowed private enterprise to continue, and tried to avoid confiscating land and businesses. Ba'athist countries did not have a command economy completely controlled by the state, such as in the Soviet Union or North Korea.
As for the nationalism angle, one of the founding principles of Ba'athism was the creation of a pan-Arab state. Unlike Marx, Aflaq supported nationalism, and thought it could co-exist with socialism. While some Arab Ba'ahists and Ba'athist-similar leaders such as Nasser and Gaddafi supported pan-Arabism, later leaders such as Saddam Hussein and Hafez al-Assad paid lip service to the idea, but never pursued it. Due to geopolitical differences, Iraq and Syria were somewhat opposed despite both being Ba'athists. Its important to remember that until 1940, Nazi Germany and Fascist Italy disliked each other more than they liked each other, due to conflicting aspirations for Austria and the Balkans.
Ultimately, Ba'athism proved ideologically incompatible with both the Western World and the Eastern Bloc, and remained part of the non-aligned movement for most of the Cold War. They were too socialist for the United States, and they were too ideologically divergent from Marxism-Leninism-Stalinism for the Soviet Union.
Ba'athism isn't nearly as common today, considering Iraq and Libya were toppled by the US and Syria is crippled by civil war. Arguably, the only 'functional' Ba'athist or Ba'athist-similar state today is Egypt.