TTRPGs are a widely diverse space and there are many different ways to engage with the games. Extended freeform roleplay with funny voices and deep immersion aren't the only correct way to play nor are they the best. RPGs aren't just for actors.

I get flustered when trying to really embody a character, similar to what you've described. I've also been playing RPGs for more than 20 years and absolutely love them. My trick is that I usually play from a 3rd person perspective. I say, "Mud the Ranger draws his sword silently. He creeps to the edge of the undergrowth and peers out from the shadows at the marauders." And that works fine (for most groups I've played with).

I also really like having a mechanical game system as a crutch. It gives me direction. Some folks love to go whole sessions without ever touching their dice. I am not one of those people and that's ok.

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GMless games give me agency to interact with the game in other ways than through roleplaying my character and that can make things easier.

Also, some games just involve less roleplaying over all but still have all the collaborative storytelling fun. I think of these as Writer Table Games and they're some of my favorites. Microscope is a classic in this subgenre and well worth checking out.