If the issue is as described in:
Cannot send an Email out of my Domain
https://forum.k9mail.app/t/cannot-send-an-email-out-of-my-domain/6028
the problem isn’t that K9 and Thunderbird are discarding or otherwise unable to send mail to another domain, rather it’s with the way your mail server is handling messages that it is receiving from your client.
K9 uses “localhost” on the EHLO connection when delivering mail to your configured mail server. Some mail servers don’t like that. What they should do if they plan to not deliver messages received is either reject or refuse them. Some, seemingly inluding yours, instead simply drop the messages into their trash (/dev/null or equiv).
Whether they think they are correct or not on the “localhost” issue, dumping the message and failing to inform the authenticated sender is rather poor form.
In the end this is an issue for your mail server support to resolve. Either they need to configure their servers to accept messages that have “localhost” on the EHLO for messages going “off domain”, or properly refuse/reject the message - informing the user.