Removable drive management

[TheDreadPirate]

When you use the laptop without the drive, is Jellyfin still running in the background?

It is. It runs automatically at every boot.

Then the problem you are having is 100% expected.  Stop Jellyfin BEFORE disconnecting the drive and disable auto-start on boot.

When you disconnect the drive make sure that Jellyfin has stopped before doing so.

Is there some easy way to make Jellyfin start only if the drive is connected?
I mean, when I disconnect it Jellyfin is always stopped, the problem is that, being my computer a laptop, there are some times which I use it outdoor and I don't have the drive with me. At boot the service starts anyway and so the next time I'll boot it with the drive connected this problem happens. So having away to prevent the service to start Jellyfin if the drive isn't connected seems to be necessary in this case. Or what's the best way to deal with this scenario?

Depends.  If this is Linux you can have the Jellyfin service ensure that a drive is mounted before starting.  If this is Windows, I'm not aware of a way to do that.

You can also have Jellyfin write NFOs and make them read only to preserve metadata.

Actually this seems to be the best way! Could you point me to a guide to do so, please?
This wouldn't prevent me to have to rescan library though, right?

You have to enable NFO saver in the library settings in Jellyfin.  If Jellyfin has already scanned your library you will need to rescan and select "replace all metadata" to trigger NFOs to be written.  After they are written and any mis-identifications corrected, you will need to ensure that the resulting NFOs are read-only to Jellyfin.  In Linux, as Efficient suggested, change the file permissions to 440 or something similar.

Selecting "lock metadata" will only prevent changes to content already in your library.  For the problem you are having, assuming you don't heed my advise to stop Jellyfin, locking the metadata doesn't apply to "new" content.