Mixing brands is rarely a problem. Some brands will fit each other nice and snug, others will have a little bit of rotational or in and out play, but functionally they all work together well. I have a bunch of different brands of sockets, ratchets, swivels, extensions, etc. Some old, some new.
I don't know if I even could make a ratchet, extension, swivel, socket combination for use, composed of all the same brand. It would probably be hard for me to make a working socket combination out of tools produced in the same decade.
I have only run into three issues with interchangeability over the years-
I used to own a couple vintage 1/4" drive SK extensions that had the male square drive tips formed very shallow compared to all my other 1/4 drive stuff. The extensions wouldn't go deep enough into many of my more modern sockets, so the ball detent wouldn't engage with the socket properly. I sold them off to solve that problem.
Some of my 1/4" drive wobble extensions don't work well with all my sockets. The wobble will occasionally want to pop out of the socket if I'm using the wobble near full tilt and I'm not applying a bit of pressure to keep the socket on the extension at all times. I'm slowly changing out those wobbles.
I have a couple vintage tools in 1/2" drive that had the original male square drive ends formed too perfectly square. The outside edges weren't beveled down enough for the tools to engage all my sockets and extensions, because some of my older sockets have slightly rounded female square corners (not off-corner engagement or the stress relieved corners you often see now). I filed down the corners of the male square drive a little bit to slightly increase the bevels and now everything works. Easy fix.