one for accounts.google.com and one for Google Calendar. They are different.

Presumably you're talking about OAuth2 authentication tokens. These are not passwords, even though Thunderbird stores them in the Password Manager. Assuming your Gmail email and the Google Calendar belong to the same Google account, there's only one Google account password which isn't stored by Thunderbird in case of OAuth2. This isn't a problem, it's just how OAuth2 works.

I receive repeated Calendar Requests for my password even though I give it the correct password

Try to delete the OAuth2 token for the Google Calendar in the Thunderbird Password Manager. Then restart Thunderbird, and authenticate with your Google password when prompted. Also make sure to give Thunderbird permission to access your Google Calendar when prompted.

Note, you may have to allow cookies for https://accounts.google.com in Thunderbird.

I did the above. It then accepted my password & 'generated' an OAuth2 token. I was able to sync Calendar. However, the irritating Calendar Request popups have now returned! Any ideas?

Is the calendar synced with an add-on, e.g. Provider or TbSync, or CalDAV?

https://groups.google.com/forum/#!topic/provider-for-google-calendar/NjGwQEBQXSs

I'm using TB 68.4.1. Relevant add-ons are: Lightning & Provider Calendar. No updates for these add-ons are available. I'm using Ubuntu 18.04. People on the link you gave are mainly using Windows. One person rolled back from TB 68.4.1 to TB60 and problem went away. So it looks like waiting for a TB fix or rolling back TB to 60. However, I'm only getting this problem on my laptop i.e. not on my Barebones PC, also using Ubuntu 18.04 and TB 68 & the same addons. Interestingly, I use the gContactSync add-on for syncing Google Contacts and that has no problems.

The Provider add-on probably needs an update, especially if Google has changed their authentication policy. Rolling back to TB 60 comes with its own difficulties, now that the downgrade option in 68 has become a complex process. Perhaps try TbSync as an alternative for calendar and contact syncing.