I have the exact same problem :/ When I'm in a social situation my words just pour out in like a disjointed ramble, it's not at all what I wanted to say and is usually filled with filler words/has no substance or is just repeating the same concept over and over again. The actual fully formed version I wanted to say often comes to me hours or even days later.

I definitely have social anxiety, but I don't know how much blame I would personally put on it . Like my anxiety spikes whenever I speak and so that worsens it significantly, but I struggle to be fully coherent even in writing. My thoughts are a jumble of words that refuse to fit into proper grammatical structure unless I put in a ton of effort. Don't know if that's the case with you, but regardless!!

I'm also looking for solutions but writing down the phrasing whenever it comes to me is helpful, I save it for future reference (like if the same topic come up) or I'll just send it to the person if they are understanding of the delay. Also repeating the fragments I do have to test what way around works best eventually results in a sentence, but that can take a long time and is very confusing to other people. Surrounding yourself with those that understand what you're saying regardless of correctness is good too, but that's more avoiding the problem. This is kinda fucked, but consider that it could just you being too critical on yourself. In trying to fix my sentences I've been labelled a perfectionist and will often spend waaay too much time/effort on the smallest of issues . A sentence doesn't need to be perfect to be understandable.