https://bw3.dev/ (@0x3b0b) your reply mostly worked as intended!
I checked my webmention.io:
* 2 replies via Bridgy Fed and Bridgy (backfeed from Twitter), and
* 1 mention directly from your original post permalink.
Your #IndieWeb reply does have a u-in-reply-to link to a fed-brid-gy/r/ prefixed URL of my permalink, however the u-in-reply-to link directly to my site is linked to my previous post (look for "2023/018/t1" in your reply content’s markup) instead of the intended post!
Try updating that direct link to use the correct URL (my original post at top of thread), add some link text to it, and resend a webmention.
It’s ok to have multiple visible reply links (e.g. this reply has them, to your post & POSSE tweet reply, at the top.).
Lastly, when you link directly from IndieWeb site to IndieWeb site with your reply, there’s no need to also link via Bridgy Fed. The direct Webmention is sufficient.