From my research, the fluid should follow this specification:
MB 345.0 A001 989 24 03
If that is the case, this liquid should be good?:
https://www.autodoc24.ro/febi-bilstein/1879380
Also, any tips on the procedure? Can this be done at home?

Thanks!

I'd go with the Pentosin stuff in the green can.
For me I just used a turkey baster, suck out fluid
every once in while, put new in. Still leaves some behind yes.
If you do that a few times. you'll have mostly new fluid.
I'm at 256K miles and not needed a new PS pump, so crossing my fingers.