Checked also the PulseAudio interface of pipewire, no delay.
So even if you need a PulseAudio server for legacy players you can still switch to pipewire.
I don’t think so, anyway you don’t have pipewire-alsa and pipewire-pulseaudioinstalled, so I wonder if pipewire does anything useful on your system.
Can you show:
OK, pipewire is installed but not active (it lacks two essential pieces).
Your system sound is controlled by pulseaudio and there is nothing wrong with that.
I would check what happens if you create a fresh test user as Malcolm suggested, just to rule out the obvious.
A few things you can try.
Are there keyboard keys to increase/decrease volume (often at or near F11 and F12 keys)? Is the action delayed even when using keys?
Open a terminal and issue top (or use your favourite system monitor), look for process pulseaudio and check that its PR and NI values are at 9 and -11 respectively.
In a terminal, from your “normal” user, issue systemctl --user status pulseaudio and look for anything error/warning/interesting, change the volume and look again.
In a terminal issue alsamixer , choose your sound card (hit F6?), then change the volume with relevant sliders there: is there a delay?
Start pavucontrol (you may need to install the pavucontrol package first) and try if you have similar delay.
You may also use pactl but I haven’t used that tool for quite some time, so let’s hope it is not needed
BTW, are you using Wayland or X11? Does anything change if you log in to the other (X11 resp Wayland) Gnome session?