I never thought about either of them, just do what feels right

Well the first bit of that is clearly a lie. 😛

Normally short climbs i stand up and in a high gear go for it. For longer climbs i sit and spin and i may stand for short periods. On very steep long climbs like on i did in italy where i had no idea how steep it was going to be until i got to the climb i stand up and grind as my suffolk gearing was a little too tall. I could have chnaged it but That would have cost money.

Ultimatleh there is no right and wrong way. If you get up without having to walk you have done in a right way.

Same applies to riding off road but the bumpier the terrian the more i stand aslo i never spin off road it is alway a low cadance effort under 60 mOstly.

climbing stood up requires fitness (obvs) but also strength and conditioning.
I used to do upto 2 hour rides on a dirt jump bike with a slammed saddle (just CBA raising it) and rode BMX for hours so thought nothing of doing 12mile trailcentre loops with 2000ft or so of climbing entirely stood up. it wasn’t the most efficient way to climb or the quickest I just didn’t find it uncomfortable.
I’m riding my roadbike a lot more again these days so I tend to climb seated on the mtb a lot more as a result. can still manage a 20min climb standing if I want to.