I can be of only limited help here because I don't understand much, lol, but I use Ubuntu Studio 22.04. Maybe this can help someone else home in on a solution.
When I boot up my system, Jack doesn't start automatically, but the following processes do auto-start:
In Ubuntu Studio 22.04, the user doesn't interact with Pipewire at all - I only know that some part of it is installed from looking at System Monitor. I interact with Pulse, ALSA (when necessary), and Jack (after I've started it with QjackCtl). I don't know what autojack is.
I've never used Rosegarden and don't have it installed, so can't speak to that specifically. I'm pretty sure, though, that I never uninstalled it - I don't think it came with the distro.
One other thing I can say is that, in the default Ubuntu Studio setup, when Jack is started, Youtube videos won't play in Firefox. Not just the audio - pressing Play makes the video window jitter for a split second and then nothing happens. Stopping Jack allows it to play. I did get them to work simultaneously somehow using one of QjackCtl's d-bus options, but can't remember how.
@smokinjo did you install Rosegarden yourself, and, if so, do you remember if you had a video playing in Firefox as you were installing it? Maybe the system got confused during installation and that has caused this issue. I know that I've had lots of similarly weird issues with 22.04 (which I didn't have with 20.04 - which had no Pipewire anything).