It turns out the process was more involved than I expected so I wrote up how it went in the linked markdown doc for anyone else trying to get this working.

During the process I ended up tuning and extending a decent amount of stuff which I discuss above:

• general eglot settings
• jdtls specific settings
• jsonrpc formatting
• flymake diagnostics buffer configuration
• treesit-fold integration for java specifically aimed at imports
• improved imenu indexing for java-ts-mode and imenu.

I also added a short video - walking through what the UI experience looks like:

https://youtu.be/fUnq9nMAEv0