See also these two related answers of mine on the DNVP and the Reichswehr.

The long and the short of it is that it appears that HOI4 has taken the declaration of monarchism by German conservatives at face value. To be a monarchist in Weimar Germany was not really about restoring the Hohenzollerns. It was rather a set of ideas that rejected the Republic and its basic legitimacy. These conservatives contended that the November Revolution was fundamentally a coup by various anti-German forces (Jews, communists, socialists, etc.) and their enablers in what became the Weimar political establishment. Monarchism was much more involved with delegitimatizing the Republic and its institutions than creating a new Kaiserreich. The Hohenzollerns often gnashed their teeth in exile that for all the various declarations of support for monarchy among the German right, there was very little in the way of concrete measures to bring back the monarchy. Weimar's monarchists invested more time and ink in bringing back the old imperial flag than they did the imperial house. And it needs to be stressed that von Hindenburg soon filled in the role of "monarch" for most of Germany's monarchists.

As for a military coup, the Reichswehr/Wehrmacht was never institutionally strong enough or confident enough to seize power for itself. There were half-baked plans to dispose of Hitler had the post-Poland war went south in 1940, but there was nothing truly concrete in place. The same pattern was in place in 1938 when the were whispers in the upper echelons of replacing Hitler with a military dictatorship if his adventurism in Czechoslovakia failed. Obviously, 1938 and 1940 led to triumphs for Hitler, so these plans went nowhere.

These failed starts underscore an important aspect of the politics of the interwar German military. While there were some principled officers and a number of the nationalist-conservative elite disgusted with the NSDAP's politics, much of the armed forces were much in sync with Hitler's agenda. It is notable that the most concrete evidence for a military coup prewar was during September 1938 when it appeared Hitler was going to initiate a broader European war that Germany's armed forces were not prepared to fight. Likewise, the 1939/40 conspiracies, however half-baked, were predicated on the notion that the campaign in the West had failed. It was not Hitler's agenda that frightened the armed forces' leadership, but rather the idea he would lose.

This was one of the key problems of the national-conservative resistance to Hitler. When you stripped away some of the more genocidal aspects of Nazi geopolitics, there was much in common with these conservatives' view of Germany's place in European affairs and Hitler's Weltanschauung. The September 1938 conspiracy's contacts in London expected Germany to receive much of the same territorial concessions in Czechoslovakia as Hitler did and a broader revision of the Versailles Treaty. The pre-Hitler Reichswehr also was quite open to planning for a war with Poland with the aim of recovering the lost territories of the East. This was of a piece of the rest of the resistance against Hitler by elements of the German right. They never really pushed an agenda that was fundamentally different from the existing Nazi government, hence their plans to replace Hitler were always late in coming and well after it was clear the war was lost.