Pixelated I tired different versions from earlier this year but was stuck on "Setting up...." Under the RCS box in settings. I think you can use different versions but this one worked right away as soon as I opened the app multiple times and then on the 2 other devices.
Are you saying with version 20240708_03_RC04.phone_dynamic you can get RCS fulling working? In other words, not only saying "connected" in the settings, but that you are actually able to send and receive RCS messages (i.e. Etouffee shows as provisioned to "true" in the Messages debug menu)?
I tried this version, after reading your post. RCS would connect right away, but in oder to get RCS fully working (Etouffee showing "true"), I still had to update to the Play Store version, as I have had to using other old versions of Messages.
I'm also on T-Mobile. (Pixel 8)
The only thing I did different was that I used the universal version from APKMirror, so I could get an .apk, rather than the arm64-v8a version, which gives you the bundle .apkm package. It's hard to imagine that would matter.