I have found marvellous success tossing powdered mimosa and rue into a mason jar with a small splash of white vinegar and a cup of water, shaking it every day for a week, filtering the plants out, and then drinking.

Could this process work with San Pedro cactus as well?

Probably not very well, cactus contains a lot of pectin/mucilage which will hold the water and you will not be able to filter it out.

I've read only of successfully doing this by a reddit user golmozak, with frozen cactus chunks blended, added bunch of water then left to sit in fridge over 24+ hours, decant top water and squeeze filter remaining water out of bottom layer plant material, then let the liquid chill another 24+ hours to let sediment settle and decant again then drink away.