Pamac icon no longer showing up in system tray

There are a number of errors there.

Jul 20 18:06:26 linux-qz0r systemd[1468]: app-pamac\x2dtray@autostart.service: Skipped due to 'exec-condition'.
Jul 20 18:06:26 linux-qz0r systemd[1468]: app-pamac\x2dtray\x2dbudgie@autostart.service: Skipped due to 'exec-condition'.
Jul 20 18:06:51 linux-qz0r pamac-tray-plasma[1838]: kf.notifications: env says KDE is running but SNI unavailable -- check KDE_FULL_SESSION and XDG_CURRENT_DESKTOP

I think that means XDG is borked. On KDE you should have xdg-desktop-portal and xdg-desktop-portal-kde installed. Check that they are and if not install them.

$ pacman -Qs xdg-desktop
local/xdg-desktop-portal 1.16.0-3
    Desktop integration portals for sandboxed apps
local/xdg-desktop-portal-kde 5.27.6-1 (plasma)
    A backend implementation for xdg-desktop-portal using Qt/KF5

This one;

Jul 24 16:28:54 linux-qz0r pamac-tray-plasma[1572546]: touch: cannot touch '/var/tmp/pamac/dbs/sync/refresh_timestamp': Permission denied

usually means you’ve run sudo pamac at some point. To fix that try this;