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Well, whatever the issue is between Arch and LightDM it is only a problem with LXQt desktop. I just installed Plasma-X11 and you can launch it from LightDM without issue. It is brutal to use on this old Netbook but it works. So this cannot be a general Qt problem. I should also point out that naked WMs like Flux and Openbox also work fine. I like LXQt a lot but really I think of all the desktops I've used it is the most likely to crash or give problems. I'm using it now and as long as you bypass the DM it is fine.  

What does the mpd.service say?    systemctl status mpd.service  

I'd probably do the same.  Probably....   But if you're correct in your theory about linux-firmware package being split into sub-package (I agree, that would be VERY high on my list, as it seems to provide a plausible explanation across all the theories posited so far), you're in a smaller subgroup than Arch users, who use LXQT, with LightDM (SDDM is the recommended DM, BTW).  If it's a firmware package, your old Toshiba may be using a firmware that very few users have installed.  MAYBE....   I'll wish you good luck getting it solved.  Stuff like this would just agitate my OCD to the point of "no rest until resolution".  At least your system is fully usable until a solution is revealed.  That's a small consolation to the OCD, but it IS a consolation.  LOL!

I tried to install wmpdart and can not get any sound out of it.  I installed mpd and think I have it configured right. Used systemd as per the wiki. The wmpdart dock app appeaser but does nothing. Am a tad stumped as to why ?   Any ideas folks ? 🤔