From my understanding, we are a Constitutional Republic, but we seem to keep floating this narrative that America wanted to spread Liberal Democracy around the world. What is the form of government a "liberal democracy" subscribes to? Or was this just a narrative we used to spread influence the way Communism did post WW1?
Constitutional Republic is a form of liberal democracy by representation. There's no huge difference across western democracies in essence , the procedural niceties however, may vary, but you can put them all under the umbrella term "liberal democracy". As regards spreading this ideology, it all boils down to expanding America's sphere of influence, increasing its political, diplomatic and economic capital. In the same manner, USSR tried to expand and push communism.