Replied to a thread by John-Mark Gurney, Dan McDonald, and Seth Wright (Twitter)

Has anyone written software to mirror their tweets to their own website? That is save static versions of them with the ability to update regularly?
— John-Mark Gurney (@encthenet) June 21, 2022

I have most of the elements to implement it, which means I should probably just do it myself. Just not sure how I'll handle the threads. Or people replying to me, and my responses. I can't archive other people's tweets, but I guess I could embed them.
— John-Mark Gurney (@encthenet) June 21, 2022

I think (from my limited time looking at it a couple years ago), the indieweb people who did something like this went the other way and mirrored from their blog *to* Twitter…which seemed pretty limiting to me for all the reasons you just brought up. (Also following…)
— Seth Wright (@Crosse3) June 21, 2022

I’m pretty sure that many within the IndieWeb space have got this working with a variety of software, particularly using Bridgy for the responses. Here’s an outline of how I do it with WordPress
I’m always curious to see other implementations.