This is not related to the Thunderbird Flatpak specifically, but rather, an issue with Thunderbird not having an OAuth2 provider for Yandex (which Yandex requires). Unfortunately, from my own cursory testing, there doesn't appear to be a way around this at the moment.
Bug 1846580 Comment 1 Edit History
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This is not related to the Thunderbird Flatpak specifically, but rather, an issue with Thunderbird not having an OAuth2 provider for Yandex (which Yandex requires). Unfortunately, from my own cursory testing, there doesn't appear to be a way around this at the moment. Edit: I found a way to get around using OAuth2. See comment 2.