Can I Install a Sub-Panel from an Existing NEMA 5-50 Plug?
If you really, really wanted to do it from the plug, then you need something called a Power Distribution Unit (PDU).  The difference between that and something you could make is the UL Listing.
However, since I supremely doubt you have anything that uses a NEMA 5-50, my advice is to tear the socket off the wall, fit a large 4-11/16” junction box there, and extend via conduit to a place where a subpanel is legal.

Where is that? Not a bathroom, and not over steps. Also, it’s illegal to block the 30” wide x 36” deep working space in front of the panel, so place the panel somewhere that won’t happen, e.g. a pathway, threshold or hallway.

The purpose of the conduit is to protect the wires from physical damage... and let you use the smaller #8 THHN wires, as they are vastly easier to work with than balky #6 cable.  It’s worth the trouble of fitting the conduit.
Now.  Inside the panel, the neutral and ground each go to independent, isolated bars.  Remove the neutral-ground bonding screw or strap. The hot is split (a big wire-nut will do) to go to both “main lugs”.  Now you can put as many 1-pole breakers as you want in the panel.  Do not install multi-wire branch circuits (shared neutral)!!!