When I try to connect, it fails with:

"The IMAP server that manages this mailbox or folder has reported an error during the operation you have attempted to perform.
The operation cannot be completed."

I've tried various combinations of the security settings.

I've set the System message reporting level to "5 - Debugging messages" but there's no more useful info in the System Messages window.

How best to go about troubleshooting this?

Are you using these settings?
You can use your IONOS email address with any email program. Simply enter your email credentials and IONOS email server settings in the program of your choice.
...
Account settings for IMAP.
Setting Value
Server address imap.ionos.com
Port (for SSL) 993
Port (TLS/STARTTLS, alternative to SSL) 143

Here are the IONOS instructions for Thunderbird. The setting will work with Pegasus Mail. https://www.ionos.ca/help/email/other-email-programs/add-a-mail-basic-email-account-to-mozilla-thunderbird/

To troubleshoot, enable Internet session logging which is located at the bottom of the General tab in Internet Options. An IMAP connection attempt will then generate a log of the communication between Pegasus Mail and the IONOS server. Its file will be stored in a directory named TCPLogs located in your mailbox directory. Review the log file for a clue into what is causing the failure. It is a plain text file so can be viewed with a text editor. It contains login credentials so do not post an entire log file without first removing them.

I'd accidentally pasted a [TAB] before my imap server details, and just assumed that the field was centre-justified.
Thanks for the help! It works now.