Why am I getting 5v on my 3.3v pin?

On those little ESP8266 mini boards the regulator failing short between input and output is pretty common, especally on the cheap clones. When that happens you get exactly your symptoms: 5v sitting on the 3.3v rail, the chip still runs because it tolerates overvoltage for a while, and the regulator stays cool because there's nothing dropping across it anymore. A few kilo-ohms between the 5v pin and 3.3v pin fits that too, since you're reading through paths into the other components rather than a dead short. First thing I'd do is figure out whether the regulator itself is the problem or something on your board is bridging. Unplug everything and measure resistance between 5v and 3.3v on the bare board. If it's still in the kilo-ohm range with nothing else connected, the regulator is almost certainly toast. If it goes high or open, then it's something you added, and you can solder one module back at a time and re-measure until the number drops. That finds a bridge under a module in ten minutes.

A solder bridge is possible, especially under the display where the pins sit close together. Get a phone camera zoomed in over the joints and check for a dull gray whisker between adjacent pins. Flux residue alone won't cause this, so the cleanup wasn't wasted but it wasn't your issue either.

As for the caps, they almost never fail in a way that reads a few kilo-ohms across rails. They either go open or dead short. I wouldn't chase that angle. Don't keep running it like this while you troubleshoot. The display being 3.3v logic doesn't mean it'll shrug off 5v for long, and the ESP8266 itself is running past spec too. If the regulator turns out to be bad, either swap it or feed the 3.3v rail from a separate regulator and skip the onboard one entirely. That's what I ended up doing on a board with the same failure and it's been fine since.

New here so take this with a grain of salt, but I had something similar on a diferent little board last month and it turned out not to be the regulator at all. My cheap usb wall wart was putting out way over what the label said, and once I swapped in a different supply the rail came back to normal. Might be worth plugging your setup into another charger or a powered hub before you start desoldering anything, just to rule the input out. Does your meter read the same on the 5v pin while it's running, or only when you probe around with things powered down?

Before you pull the regulator off, do what we used to do back in the day and just lift its output leg off the pad. Feed the board and check the rail again. If the 3.3v side drops back to normal with that leg floating, whatever is dragging it up is your own wiring or a module, not the chip. If it stays high right at the lifted pin, the regulator is done and you can order a replacement without any guesswork. I've saved myself plenty of desoldering grief doing it this way, especially on boards where the part sits tight between other components and comes off with the pads if you're not careful.

Worth checking if one of those modules has its own little regulator on it. I had a sensor breakout do this to me once, wired it up wrong and it backfed voltage straight into the rail from the other side. Pulled that one module off and everything read normal again. Also don't count on the ESP8266 itself lasting, mine seemed ok for a few days and then started random rebooting. The flash chip is the part that ussually gives up first, and that's the one you can't really replace.

One thing to keep in mind with that resistance reading is that measuring ohms on a circuit full of陶瓷 caps and chips gives you a mushy number that means very little, since the meter sees a coil of different paths folded togather and the capacitor charging skews it besides. Switch the meter to diode mode and probe both ways between the two rails instead, and the direction that conducts low tells you which pin is feeding which. I chased a similar mystery rail last year and the diode reading pointed right at the video driver on a little module I'd have sworn was innocent.