The first picture looks like a fluid master, a low cost, DIY replacement, can be noisy.

Fluidmaster has different replacement kits...I recommend the “replace all” kit, vs individual kits for each component.

Fluidmaster used to, may still does, advertise, “if there is a leak you will hear it” or something similar.

I recommend against replacing the toilets, they maybe worthy of having parts replaced.

FWIW, if you replace your toilets, you may have to use lower water use toilets, some of the low usage toilets do not clear the bowl, and or are noisy.

It's probably the flush valve seal. That's the round black gasket at the bottom. Very easy to replace.

Thanks everyone! I've been monitoring it more closely recently and now can confirm that the water in the bowl is also leaking/lowering slowly throughout the day. Unless it's normal to notice after flushing a toilet that the water level goes higher then before it was flushed?

In the case of the tank and bowl slowly lowering and having to refill themselves, what part(s) should I be repairing/replacing?

If it’s the flapper letting water leak by that could be a simple fix. Turn off the water supply then flush to let as much water as possible out of the tank. Then take a cloth and wipe the flapper valve and the gasket it sits on. Then take a dab of Vaseline and smear it on the gasket. That’s worked for me several times

In the olden days, there were tablets to determine if the flapper was leaking.

Re what to repair/replace...Replace everything.

You can put a few drops of food coloring in the tank and see if it ends up in the bowl...

Should I go through the process of replacing parts until I fix the leak or is it better to just get a new toilet at this point?

You can either spend a few dollars for parts & learn how to repair a toilet now.

Or you can spend a lot of dollars for new toilets and learn how to repair them a few years from now.

There's no flapper (does anybody see a flapper there? No, there is not a flapper). I repeat, it's the flush valve seal. The black gasket at the bottom of the tube. It costs a couple of dollars and takes about 30 seconds to replace.

Replacing the toilet because of this is akin to having an electrician rewire your house because a light bulb burned out.

Thanks for the info and advice! Yes, I agree that replacing something you can easily and affordably repair is silly. I just wasn't sure if this was one of those times where, because of the age of the toilets, that it might be better to upgrade to a new brand/model, like a Toto toilet or something nicer. I definitely am the type who prefers to repair vs replacing and especially with something mundane/utilitarian like a toilet.

I purchased a Mansfield flush valve seal for $4 and installed that today. I think it was a replacement that was well overdue as when pulling off the old seal, it immediately started to crumble and melt in my hands. So far, everything seems to be working great with the new seal and I am not noticing any leaking. Thanks for the help!