Choosing optimal TX power for a particular device

I have a IPQ4019 device with SKY85309-11 fem for 2.4G and SKY85728-11 for 5G.

Should I take any care when setting TX power in the luci interface? Any chance that setting it too high or low may degrade performance or cause hardware damage?
With region set to US it goes as high as 500mW.

As low as possible (good coverage) and 5Ghz should have ~+6dbm higher tx power.
For example, start with:
2.4 Ghz @ 9 dbm
5 Ghz @ 15 dbm
If coverage is too low, go for 12 dbm and 18 dbm

A rule of thumb (and in some areas - law) using only enough power to cover your site/use-case is necessary.

Unlikely.

If the OEM has accounted for the external gain properly in their calibration data (both board files and ART), it should work transparently for ath10k. The more you go from big/ reputable OEM, who knows how to do this properly (and to get the necessary certifications) to quick-hack designs using external frequencies shifters or power amplifiers, the more likely to enter difficult territories.

And yes, it possible to damage the hardware by running it outside of its specifications. If the OEM did their job according to the SOC vendors requirements (providing proper board files and ART), setting out-of-spec signals shouldn't be possible - if they didn't, anything can happen (this is often a case for vendors who use WLAN chipsets for non-wifi frequency ranges (e.g. 900 MHz) using external frequency splitters and only accounting for this in their custom (shim-) driver interfaces (unbeknown to the kernel/ wireless driver)).

They're not doing anything that crazy but I don't feel like they put proper engineering efforts into this thing, the stock firmware even says it's a "Qualcomm IPQ40xx/AP-DK07.1-C1".
Is there any way I can check if they accounted for the gain properly?

Sure, use a RF power meter.