It’s not very complicated, in my opinion. LMS can be installed inside HA as an add-on. I also have a separate music server (Navidrome) but I just pointed LMS to the same directory that Navidrome uses, and boom, control of all my music through HA.
The only caveat that I can think of is that your HA install needs to be able to see your music directory. In my case, I run HAOS in a Proxmox VM, so I just installed the Samba Share add-on.
The thing about Arsenal is they always try to walk it in