This could change that of course but the emails don't have information in them because of Gmail.
Senders are already going out of their way to ruin the user experience just to stop Gmail slurping up all the information.
One big part of raising this mysterious and possibly just a myth "quality score" is to increase your emails open rates and especially your click-to-open rate. Basically, the more people you get to open your email and then to click through to your website, the better that Google will think your emails are performing and the more likely they are to appear in the inbox in the future.
Plus, clicking through an email provides tracking information not only to Google, but also to the site you clicked through to, which helps them with their marketing campaigns or whatever else they are doing with their tracking info.
There is an entire pseudo-science that email marketing people use in attempts to increase deliverability and "inboxing" in Gmail and a lot of it just comes down to "get more people to click through to your website", and it does appear to help, at least anecdotally.
https://daringfireball.net/linked/2020/06/01/product-info-in...
E: I should have acknowledged the rest of your post, sorry! I did read it, I've just got nothing to add as it's new information to me, thank you for the info! Didn't mean to come across as dismissive there! :)
So I'm not sure if there is such a thing as a "quality score", but there certainly is a machine learning black box.
Also remember when you could respond to social network messages via email? It was so useful! You don't even see the content anymore haha (that one's almost definitely to draw you back to the site tho)