Don't quibble over $8 worth of wire
What you're asking is, "Do the tap rules allow me to continue this with a lopsided #12/#8 feeder?" Technically yes, but why bother?
The feeder is alright right now under 240.21(B)(1), but only because of the breakers in there are the size they are. If someone swaps them out to tandems (and why on earth wouldn't they?) instantly that #12 feeder is too small. By using the tap rules you are shifting responsibility onto the next plumber or furnace guy who happens to need a slot. Those 2 spaces will be a magnet for folks like that since they're the only 1" breakers in the house.
For 50A, #8 copper THHN will suffice (because it's 75C wire unlike Romex).
Grounds good.
Ground is carried to the other box by the Rigid Metal Conduit (RMC) nipple. And that's fine.
Neutrals bad. Very bad.
What is not fine is the failure of the neutral to come over to the disconnect enclosure (it is hardly a sub-panel). Something is seriously wrong here. If the 2-space thing powers a 240V-only load, the neutrals are fine (nonexistent) but the breakers need to be handle-tied. Otherwise neutral needs to come here as #8 and go back as dual #12 (or single #12 if the circuit is a MWBC or 120/240V).
However if it is MWBC the breakers need to be handle-tied, which means, the same model lol and the correct model for this panel. 1" breakers are NOT interchangeable among brands! If it is 120/240V, then it needs to be a 2-pole common trip breaker.
Get a new subpanel!
Hack that disconnect off the wall and save it for when you need an actual disconnect. Replace it with a 24-space panel fed by #8 Cu THHN wire off those thru-lugs. You can use the same Rigid offset nipple if you want, or they make bigger ones or you can make longer ones with EMT conduit. Definitely stay metal because it handles ground for you.
I say 24 space because on anything smaller you'd probably run out of spaces before you run out of amps. Since residential breakers are typically very oversubscribed.
However even better
would be to fit a subpanel that is a candidate to become your new main panel. Because down the road you are likely to say "Gosh, it's time to replace that main panel". When that day happens, you will either be looking at a $2000 main panel replacement... or.... simply moving the service wires to that subpanel you installed back in 2022 because you listed to Harper LOL, maybe $500 of work.
In this plan, I would definitely go with a 40-space panel, because modern houses really need that many. Don't fuss too much about main breaker size; 200A is a safe choice, it can always be downsized if it becomes the main breaker (which it might not).
I would put it right next to the existing panel, like 2" over from it, or even closer if the panel covers will fit. And have a number of "pass-through" nipples (like that one) up and down the sides of the panels, to make it easy to pass wires through. Mind you, that curved conduit will be in the way, so I'd back the wires out of it and cut it to have it enter the new subpanel instead.
Once you're there, with a huge subpanel next to the Pushmatic panel, you slowly move all your "Lighting Area" circuits over into the subpanel, pretty much as those two circuits already have, but with neutral brought along too. At that point, there are 2 possible endgames.
Have a pro come in and remove the Pushmatic altogether and reroute the service wires to the new sub.
Have a pro fit a 100A Pushmatic breaker into the top position of the Pushmatic panel. Run #3 Cu or #1 Al wire from that breaker to the new subpanel. At this point all the other breakers are gone from the Pushmatic panel, and it's just a main breaker enclosure and a junction box. Having only a single breaker also eliminates all the problems of a "Rule of Six/split-bus" panel.
"That was cheap and easy"
Why don't I have you DIY-installing breakers in the Main Breaker section of a Pushmatic split-bus panel? Because Pushmatic breakers are bolt-on, and the screws are always-hot. So you need to know what you're doing.
