New OLED seems dead, how can I be sure? I bought this 2.8" OLED from Aliexpress a few weeks ago: https://www.aliexpress.com/item/32988174566.html?spm=a2g0s.9042311.0.0.72304c4dAWcHG8

And after a ridiculous amount of searching for a datasheet, I came across this one that seems to match the board I bought: https://www.buydisplay.com/download/manual/ER-OLEDM028-1_Series_Datasheet.pdf

Wiring up pins 1 and 2 to ground and 3.3V on a breadboard, I'd expect something to happen with the display, but I get nothing. The display is in 8080 mode, so I wire everything up to a standard UNO board and power everything on. Still nothing. Try changing the power to 5V, no joy.

During my testing, I noticed the back of the display is getting hot. Not sure if that's a good thing or not yet.

So what's the best way to 1) determine if the datasheet I found is correct? 2) check if the OLED is just broken? I don't have a ton of experience with these displays yet, so I'm not sure if just powering the thing on should net some visual response.
The datasheet you have found is not for the same display. Yes, it's similar, and yes, it has the same actual OLED display unit on the board, but the PCB is different. So you cannot assume that the pinout is the same.

The fact that it's getting hot tells me that you have probably wired something wrong and you are injecting voltage into it somewhere where voltage doesn't want to be injected.

To find if an OLED is working you have to actively wire it up.  With an LCD you can just give it power and you should be able to see some visual indication that it's working (back light, some shadowing of the display matrix, etc). But with an OLED you can't do that.  An OLED is made up of a matrix of LEDs which are either on or off. By default they are off, and when they are off it's no different to there being no power. That's the big benefits of OLED displays - low power consumption and true black.

To get any kind of indication that the display works you both need to wire it 100% correctly and program the Arduino in the right way to actively drive it by displaying something on the screen.  My usual test program when working with a new screen is to simply print millis() in the top left corner.