So why did > ever become greater and < be less than? Doesn’t it also depend on how your text is written? If people reading from right to left or down to up vs left to right and up to down, means it’s reversed.

Yes. > is "greater than" because you're reading left-to-right. 12 > 9, read: "twelve is greater than nine". When reading in a right-to-left script, it's the opposite, but because of how the BiDi spec works, the same Unicode character is actually used for the same semantic meaning, rather than the appearance. Taking the exact same block of text but formatting it right-to-left (using directional isolate characters) yields "⁧12 > 9⁩", which is still read as a "greater than", just from right-to-left.

Hopefully that makes sense.

So yes, if you copy the > character and paste in any directional environment, it will retain its meaning of "greater than".

Edit: on my phone, the RTL portion is not formatted well. If you can’t see it, try a browser.