I will share information on this issue that has arisen from me.
I noticed recently on one of the computers that the mail stopped loading in Mozilla Thunderbird and the following message was displayed:
The IMAP server “…” does not support the selected authentication method. Please change the “Authentication Method” in “Account Settings | Server Settings”.
Before that, the mail was successfully downloaded, nothing changed in the Thunderbird configuration and on the mail server.
On a neighboring computer with similar parameters, there was no problem.
As I found out, the problem was in ESET NOD32 Internet Security and after turning off its protection (not a firewall) – the problem disappeared.
It’s amazing that the problem did not appear right away, during mail setup for example.
Since this computer was changing hardware and reinstalling the OS, and also mistakenly installed ESET NOD32 Internet Security, I did not investigate the reason for the blockage, deleted it and installed ESET NOD32 Antivirus, which was always on this computer, with the hope to continue to investigate the problem if it repeats itself, but after that it disappeared and did not appear.