I have been searching through models and templates and can't make it work.

Here is the setup:

I create a new Discussion group: NewDiscussionGroup
I give it an alias email: email@domain.com
I turn on the "Send messages by email" option.

That gives me expected behaviour and in effect, I have an email discussion group I can use for different interest groups.

But, I have 2 deal breakers so far:
1. reply-to in sent emails is: "Full Company Name NewDiscussionGroup" <email@domain.com>
2. the usual branding footer "Sent by ...."

What I would like is to have reply-to value set just to: "NewDiscussionGroup" <email@domain.com>
and no branding footer.

Any help on that would be much appreciated.

I have been searching through templates and models and can't seem to identify which ones are used to send email messages from discussion groups/channels. The closest solution I think I got so far would be modified automated action offered in this answer:
https://www.odoo.com/fr_FR/forum/aide-1/question/how-can-i-change-the-from-and-reply-to-email-address-of-all-my-helpdesk-emails-going-out-instead-of-the-user-who-replies-140455

But I would rather not overcomplicate things and put another overhead on the system. Is there a way to create a new model/template combo for those particular emails sent from that particular discussion channel and then make necessary changes/customization only there?

Or perhaps even simpler, just thinking her out loud, modify "Default values" array in email alias used for that channel? If I click on the email provided for that channel, it opens a record of it and there is an option of entering some default value array there. Just not sure how that works, but I can imagine there might be an option to put some "reply-to" variable in that field and hard code the proper value just for those records.