Finally, TIL, what can all be the reason for systemd services to hang indefinitely. The internet is flooded with numerous reports on this topic but no clear answers. So no more uselessly marked workarounds like: systemctl daemon-reload and systemctl-daemon-reexec for this scenario.
The scene would be something along the lines of:
rrs 6467 0.0 0.0 23088 15852 pts/1 Ss 12:53 0:00 | | \_ /bin/bash
rrs 11512 0.0 0.0 14876 4608 pts/1 S+ 13:18 0:00 | | | \_ systemctl restart snapper-timeline.timer
rrs 11513 0.0 0.0 14984 3076 pts/1 S+ 13:18 0:00 | | | \_ /bin/systemd-tty-ask-password-agent --watch
rrs 11514 0.0 0.0 234756 6752 pts/1 Sl+ 13:18 0:00 | | | \_ /usr/bin/pkttyagent --notify-fd 5 --fallback
The snapper-timeline service is important to me and it not running for months is a complete failure. Disappointingly, commands like systemctl --failed do not report of this oddity. The overall system status is reported to be fine, which is completely incorrect.