User Agent: Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Firefox/60.0

Steps to reproduce:

version: 1:60.8.0-1~deb10u1
Whenever I want to load new emails from my gmail account a web browser window with password entry pops up. I enter my email and my password and finally I acknowledge 'grant access' for Thunderbird but T. writes 'can not authenticate'. The password is correct, I have tried it with my webbrowser. Access for unsafe applications is enabled in the gmail settings so I wonder why this web UI login dialogue is necessary. The problem has occured after changing the password of estellnb@gmail.com.

You need version 68.2.1 or (in progress) 68.2.2 https://getthunderbird.com/
I'm not sure which are/will be available via debian

I'd bet there is some Add-On installed that make some trouble on this. I've seen such issues from time time and likely always some extension was responsible for the problems. I've no problem with my GMail account so it's obviously not a Thunderbird issue in general.
Please disable the all extensions and switch them on again part by part. And if this all is not working please try again with a new profile for your user. Please backup your old profile first!

The current ESR version of TB will be available also for Buster and Stretch, I'm working on making this possible. But it will take some more time as my time is unfortunately a bit limited currently to work on this.
BTW: 60.9.0 is available for Buster and Stretch since about a month.

This would be about Bug 1592407, not an addon.
It's been mentioned on tb-planning, but it looks like maybe it didn't get mentioned on tb-drivers

Wayne, your are sure I'm the person you need some more information? If the reporter is using OAuth2 can only answer the reporter itself. I haven't experienced any problems with my GMail account for a long time. Even not with the previous ESR version 60.x.

I have disabled all extensions; now I get something different instead of acknowledging that Thunderbird may have access:
Google
400 That´s an error
The requested URL was not found ...

I am sure that it has something to do with changing my password. I was asked to changed it because someone else would know it. It is almost sure that the problem stems from Google. However there seems to be no way to contact support personnel of Google.

Well it is an error that Thunderbird does something different for gmail accounts. It works well with K9-Mail on my mobile phone. If I have activated 'unsafe access' then Thunderbird can access the emails just the same way as from any other imap server.

I have changed it from OAUTH to password normal and now it works.

Carsten, do you understand the email I sent?

I understand that the issue is probably within versions before 68.2.1, but I don't understand why you was needing some more information from me.

Anyway, 68.2.1 is on the way to Debian stable and old-stable. But some more days it will take as we need to coordinate some other packaged Add-Ons for these releases.