I also used a backup to fix my issue, and in fact used my backup to trouble shoot. I was the first one to report the issue on the AMP github page Version v4.13.3 is making HA fail · Issue #2579 · alandtse/alexa_media_player · GitHub To re install the previous AMP version without having to restore the full back up you can use the HACS ingegration as shown bellow
You might not have enough time to do it before your system shuts down. What you could do is right after your system boots up, go to “devices and settings” select the Alexa Media Player integration, click the 3 dots, and select disable.
Once disabled I would reboot again, and at that point your HA should be stable, and you should be able to re install the previous version of AMP