It's actually not entirely that. Google appears to have some kind of unpublished "quality score" that is applied to emails received in a Gmail account, and it uses this score to determine if the message will appear on the inbox tab or in the promotions tab (or worse, the spam box).
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.
My knowledge originates from this post if you'd like to evaluate the source. The reason as to why is a theory in the post too so it's not exactly a real source, it's my source.
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! :)
For what it's worth, I'm a google workspace administrator and we've had issues with legitimate business emails going to our spam folders. We used various tools in the workspace admin console to whitelist the sender, but their mails kept going to our spam. We contacted google support, they verified our settings were correct, then kind of shrugged and said they can't explain why gmail flags things as spam. They clarified that it wasn't just that they weren't allowed to tell me, but that it was literally impossible for them to know.
So I'm not sure if there is such a thing as a "quality score", but there certainly is a machine learning black box.
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.