This is the correct answer. What's really happening is that the to/of has instead become a singular schwa sound, which is an unstressed, non-specific vowel sound we use in English (the most common one in fact) that gives emphasis to other parts of the word. Think of e in kitchen or o women. We don't actually pronounce them as e or o. Without schwas English would sound quite robotic, it also makes English quicker and easier to speak.

Unfortunately that doesn't answer whether or not he was trying to say "to" or "of". But thinking about it, when would you need to say "transition of military power"? That's not something you really say. Unless he's saying the inauguration is going to be a show of military strength, on Biden's part, which would be quite the provocative thing to do, even for MSM standards, no? It seems like the logical thing to say is "transition to military power", because transition generally collocates with to, and not of. Someone would only really say transition of military power if they specifically wanted to frame it that way. Otherwise, transition to military power is the natural thing for a native speaker to say.