Slight brown tint when starting cold water from tub faucet?
I cannot add a comment so I’m placing it here?

If you want to try and pinpoint if it’s that single line or fixture or possibly a whole house issue. I’d start by seeing if any other locations, after sitting a couple days has this same issue or not. If the rust/corrosion still only settles at the tub fixture you would (likely) narrow down your culprit.

Im just reaching here. Is this tub at the end of the line of your plumbing? And if so are you using other water lines in the vacinity? That would keep water moving to or past the take off line to the tub? Or depending how you water lines are set up. If you have your supply line running the length of the house and 1/2” take offs from there at the room location split to the fixture. If this line to the tub is the only one coming off the supply line from the underside of it. It possibly be actaing as a rust knock out and as rust passes past this line the sediment could drop down and collect up.

If you can do some further investigating and show/explain your water supply set up and trouble shoot a tiny bit more, it would really help further narrow down a potential issue and help the community have a less broad and more informed answer. Hope this helps