Loud rumble/clicking when upstairs toilets flush

Hey! Hoping to get some plumbing advice for a homeowner.

Background if it helps: we purchased this house in May of this year. House was built in 2009 and only remodeling or plumbing added was to the basement in 2012 (adding a 3/4 bath when finished). There are two full baths upstairs, a half bath on the main level, and the the 3/4 in basement. One of the toilets upstairs we replaced new in August of this year, the other toilet is original.

Over the last several months, we’ve noticed that when the upstairs toilets flush, there is a rumbling/clicking sound that comes from what I assume is the “tree” or pipes in the wall on the main level. Sometimes it sounds like a “popping”. The noise is significantly louder when there is anything more than a #1 being flushed, and more toilet paper means louder noise. You can hear the “swooshing” of the water, but there are no leaks anywhere in the house from what we can tell.

I’ve been reading that this can have something to do with the toilet valves, though I have a hard time believing that it would be both toilets - one of which is new. I’ve already read something about a “hammer”, but to be completely honest I don’t understand what that is or how that would work or if it’s a one-toilet or whole-house thing.

Thoughts? Advice? If it is a loose pipe, how screwed are we?

Edit - link to sound here