Your software
My Mautic version is: 6.0.6
My PHP version is: 8.4 (Debian Trixie)
My Database type and version is: -
Your problem
My problem is:
Starting with Debian Trixie the libc-client-dev (libc-client2007e-dev) package required to build the imap ext is not provided anymore.
Research revealed: IMAP extension moved from PHP Core to PECL - PHP 8.4 • PHP.Watch
Root cause:
The underlying C library that the extension depends on has not received any updates since 2018.
Thats 7 years now. 
docker-mautic worked around by pinning to debian bookworm: fix: Unable to locate package libc-client-dev by kiart-tantasi · Pull Request #441 · mautic/docker-mautic · GitHub
There is the webklek/php-imap PHP implementation: GitHub - Webklex/php-imap: PHP-IMAP is a wrapper for common IMAP communication without the need to have the php-imap module installed / enabled. The protocol is completely integrated and therefore supports IMAP IDLE operation and the "new" oAuth authentication process as well.