I would like to be able to use the Let's Encrypt extension to add new certs to the "list of certificates in server pool" and make use of a Let's Encrypt (LE) cert as the "default certificate" for domains that have not added their own specific certificate.

I thought this was already possible, but was incorrect. I added a LE cert on the Tools/Settings > SSL/TLS Certificates page, and made it the default certificate.

However, I used a different certificate to secure the Panel and the mail server. It appears, in that case, the LE cert will never be renewed.

I would like to have the LE certificate renewed if it's set as the default cert even if it is not used to secure the Panel or the mail server.

I don't consider using LE certs a good idea to secure the mail server because some e-mail clients, especially Apple clients, break when the cert is changed or renewed, causing end user support problems. Due to this, I use a different cert, that lasts for 2 years, to secure the mail server, to avoid that issue happening frequently (every 90 days). See...

https://support.plesk.com/hc/en-us/articles/115004756974-Mail-users-with-iOS-and-MacOS-devices-cannot-access-mail-after-certificate-renewal-on-Plesk-server-Cannot-Verify-Server-Identity

Thanks for your consideration.