[PROBLEM] Bootup/shutdown issues, how to debug

[vinnn]

Strange. I agree, the logs look like startup logs upon closer inspection, but the logs have been taken at the exact time, I shut down the system.

It doesn't seem  that I have any issues with boot, but shutdown, especially after I enable Bluetooth. How can I debug the shutdown process? and how can I debug the "Bluetooth issue"? when I enable Bluetooth, I can't shut down from the moode GUI, only by issuing "shutdown -P now" over ssh.

Firstly I'd rule out any possible web browser issues by deleting your browser's cache and try again and also try a different web browser.
If this behaviour persists across browsers then there may be some filesystem corruption affecting certain files and causing the flushing of the fs cache to hang on shutdown. You say you have some sort of power switch attached to the Pi, if you're in the habit of hard powering-off the Pi without shutting it down you can expect filesystem corruption eventually.
Secondly, try a new install on a different SD card if you have one handy.

For looking at shutdown logs the system journal is not persistent by default on RaspiOS and in turn Moode so any journals are gone after shutdown/reboot.
You can change this by setting the journald storage to persistent in /etc/systemd/journald.conf, for example...

Code:

sudo sed -i 's/^#Storage=.*/Storage=persistent/' /etc/systemd/journald.conf
sudo reboot

... rebooting to take effect, subsequent shutdowns & reboots are then kept in the system journal.

To put it back...

Code:

sudo sed -i 's/^Storage=.*/Storage=volatile/' /etc/systemd/journald.conf
sudo reboot

To view system journals use the journalctl command, e.g.

Code:

sudo journalctl --list-boots   #shows times of previous boots and the boot number
sudo journalctl -b -1          #shows logs from previous boot
sudo journalctl -e             #skips to the end of the system messages (aka syslog)
sudo journalctl -ek            #skips to the end of kernel messages

You should then be able to see the shutdown messages in the journal for the previous boot.
At a guess it's something unique to your install or the web browser as described above.