I've taken a look at the idnet site and it seems that they give out fixed IPV4 addresses and a /48 for IPV6 - so rebooting your router won't have changed the address.
One question I don't think we have addressed is whether the problem only occurs on this one specific email address at idnet (you say you use Tbird for others such as gmx). To eliminate that possibility, is it possible for you to set up a completely new address with your ISP and test connectivity to that?
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So - try https://pingability.com/mailtest.jsp BUT NOTE that you must give them your email address and password. For obvious reasons I suggest strongly that you only do that only for your new test address, not the address you are actually concerned about.
Try also https://www.wormly.com/test-smtp-server they have both SMTP and POP3 tests (but no IMAP that I can see)
Right. New address. Tried pingability. It timed out. :-/
Set up test address in Evolution (disabling the other address I had there) and it kept asking for the password so there really are multiple logins being attempted at least.
Bev