I haven't done any more research than this, but after having the same problem,
I uninstalled the Tailscale package, make a backup of the configuration after the upgrade to 24.03, and then edited the configuration file to remove the <tailscaleauth> and <tailscale> entities from the backed up XML config file and reloaded it as a Restore.
I then created a new Auth key for it in the Tailscale Admin and proceeded to reinstall Tailscale.
This time it worked. Comparing the XML entities from XML file from the 23.09 version of pfsense with the one from 24.03, there were only two changes (apart from the different Auth key in the <tailscaleauth> entity:
In the v23.09 backup, the entity contained these values:
<tailscale>
<config>
...
<acceptroutes>on</acceptroutes>
...
<syslogenable>on</syslogenable>
...
</config>
</tailscale>
After reinstalling the package in the v24.03 instance, these entity attributes were blank/empty.
I have other things to work on with deadlines, so I don't have any more time to investigate this further.
But I'd be interested if someone just wanted to edit the config.xml file to remove these two values and try it again without having to remove and reinstall the package.