You can try turning up the bed temp, lowering the z-offset to get the nozzle closer on the first layer, or increasing the first layer flow in your slicer. For me the purple glue sticks on a glass bed worked, but sounds like that’s not working for you for whatever reason.

Another trick I’ve seen people use is adding some circles to hard corners like that in the model that you can cut off later.

If PETg (which is where I've most commonly had warping), make sure Filament is very well dried. Try both raising or lowering bed temps and bigger brim.

Also, for funsies, try rotating print orientation 45 degrees if you can. Might shift stress away from corners to sides.

So I gave it another try with the black filament after doing some additional adjustments and was still getting the same issues. I then swapped to a brighter filament so that I could get a better picture and now it’s laying perfectly flat. I’ll let it continue printing to see if any other issues pop up, but it’s weird that one filament was lifting but an older spool works fine.

Cleaning is a good suggestion. I'd start there.

Also, that kind of looks like the cheap black textured plates that come with some printers. I thought the people talking about pei sheets were over-hyping but honestly they are really much better. It's not a silver bullet but pla sticks soooo much better to them.

For pla it's overkill, but for tricky stuff build adhesive can help. I had good luck with vision miner. It's expensive but it's been buy once, cry once because it has lasted a really long time.

Given all you've tried I can only conjecture that this may be a print temperature issue, especially since you already tried adhesive. What material are you printing, and at what temperatures for nozzle and bed?

You may also find that your printer's sensors are not reporting temperature accurately. Mine sure isn't and never has, at least on the bed, and it consistently reads about 5 degrees high versus reality if you poke the surface with an external temperature probe. This isn't a big deal only so long as you know to compensate for it. The thermal conductivity of whatever your print bed material is may also force you to compensate, i.e. a glass plate will not perform the same as a steel one and may require a boost of a few degrees and/or allowing it to cook longer during the preheating phase before you start your print.

I print on a sheet of cheap Kapton tape with a later of even cheaper hairspray on it (Aqua Net, if you must know), "65" °C bed temp for PLA (60 in reality) with a first layer temp of 215 for regular PLA, and 210 for "rapid" PLA blends. My sharp corners stay put.

So I gave it another try with the black filament after doing some additional adjustments and was still getting the same issues. I then swapped to a brighter filament so that I could get a better picture and now it’s laying perfectly flat. I’ll let it continue printing to see if any other issues pop up, but it’s weird that one filament was lifting but an older spool works fine.

Because nobody said it yet: wash your bed with warm water and soap to remove any residue (especially oily fingerprints)