Mac OS, Firefox in sleep mode

So does it appear to be closing tabs, or shutting down as mentioned in previous support.mozilla.org/questions/1599468 (or both / depends)?

Do you have to restart it? Or it seems to restart on its own? Or it's already started when you wake up the device?

I assume it restarts, as it displays the two start up tabs.

Then please follow the steps in support.mozilla.org/questions/1599468 to see if there are any crash logs potentially captured.

Otherwise that sounds more like the whole device shuts down and restarts instead of sleeping, and restores after starting up. The next time you encounter this, click the Apple menu from the top left corner while holding the Option key, and then choose System Information. Click Software in the left-hand column. The time since the last reboot is displayed next to ‘Time since boot’ in the right-hand section. That might help identify if the underlying system rebooted. (But won't tell if just a profile got logged out, though.)