What is the maximum number of cassette teeth compatible with Shimano 11 speed 53-39T, 52-36T & 50-34T crankset? I want to upgrade my bike which can speedup in flats but also climb efficiently in slopes. Can someone give the maximum number of teeth that would be compatible with those 3 cranksets, if I where to use a MTB RD? Also, I prefer Shimano as they are abundant here in our area and way cheaper than SRAM.
The rear derailleur mostly determines maximum cassette sprocket size. The absolute size of the chainrings does not affect it, but the difference in size between them can limit it.

The largest cassette sprocket size is determined by two rear derailleur specification: the  max sprocket size of course, and the total capacity.

Total capacity = difference in min/max sprocket teeth +  difference in min/max chainring teeth. It's basically a measure of how much chain slack a derailleur can take up.

However, for standard modern compact and subcompact cranks the chainring size difference is always 16 (52-36, 50-34, 48-32 etc), so normally the rear derailleur max sprocket size specification practically limits what cassette you can use.

If you combine an MTB rear derailleur and a road crank, the total capacity might limit the max cassette sprocket size to less than the derailleur's max sprocket spec, because MTB double cranks typically have a size difference of 10 teeth rather than 16 (at least Shimano's recent offerings do).

If you use a derailleur hanger extension or other method to accommodate a larger cassette sprocket, then total capacity does need to be taken into account.