It's possible to natively integrate your Google calendars with Thunderbird 102.* . However, it's not possible to open a shared Google calendar, you're only presented with your own calendars to open. Adding via the calendard URL doesn't work.
@schnuffitoI think you can get this feature with the "Provider for Google Calendar" plug-in for Thunderbird.
HOWEVER, there are some caveats! I have had difficulties accepting/rejecting meeting requests, dismissing reminders, synchronizing, etc. with the "Provider..." plug-in. So much so that I have had to make my Google Calendars read-only in Thunderbird.
Native Thunderbird support for (OAuth) Google Calendar is great and doesn't have those issues, but the lack of support for shared-with-me Google Calendars means we're stuck with the Google web interface for now.
If only this useful idea could get the same attention as, say, support for certain icon themes...
Synchronisation of shared Google calendars is literally one of the features that should be implemented but is missing. Furthermore, the extension mentioned by @digitalfix (Provider for Google Calendar) is unavailable for Thunderbird Beta and Nightly, so it doesn’t really solve the problem (currently). Unfortunately, the incompatibility isn’t the only problem – Google calendars with thousands of events in Thunderbird (its stable release with the extension installed) make it laggy, and the sync takes ages. I’m not sure if that’s possible, but the easiest way to optimise the whole calendar synchronisation would be to select the synced number of days into the future and past and temporarily sync currently viewed days. I hope that synchronisation of shared Google calendars will be directly integrated to Thunderbird. Using Google Calendar site is a pain and Provider for Google Calendar extension isn’t available for Beta and Nightly channels, plus it makes Thunderbird laggy (though it might be Thunderbird’s fault). Making this feature not only integrated, but also making it work smoothly and quickly would be greatly appreciated.