First of all, of course you should watch the Star Wars shows! They are an integral part of the franchise and they add a lot the the characters, the world-building, and fill in the gaps between the trilogies. I would recommend watching all of them, maybe apart from Resistance, since it doesn't connect to anything and it's not a must-watch if you want to understand what's going on in the galaxy.
Here is the order in which I recommend to watch them all:
The Clone Wars
Rebels
The Bad Batch
Obi-Wan Kenobi
The Mandalorian (seasons 1+2)
The Book of Boba Fett
The Mandalorian (season 3)
Ahsoka
Andor (a prequel to Rogue One focusing on Cassian Andor)
Visions (non-canon)