I think DrSparks has it: the fact that one side of the breaker gets hot only supports it IMO. Though it might still be a bad breaker, and you do have work to do there.
See where 2 of the breakers are half-width, yet the breaker knockouts are full-width? There's lots of room for curious fingers to get in there and find an energized bus stab.
Those can easily be changed for full-width breakers. And, you may be in there replacing the 50A breaker anyway, so it's just 2 more of what you're already doing. Now's the time.
I say that since those breakers are $10, notwithstanding COVID shortage pricing, and it's the same to change all 3 as only one.
The thin breaker has the distinctive design langue of GE - both with the thin 2-pole (notably not a quadplex) and with the body and handle shape. On that assumption... The breaker you need is probably a THQL250 for the range, THQL230 for the 30A thing, and THQL2XX for the one on the right, with XX being the number on the breaker handle. However if the GE panel is every old, the THQLs may not fit, and you'd need to use the Eaton CL250 and CL230 (note the CL which is not the same as CH or BR or C. Call around to actual electrical supply houses for an Eaton dealer that sells Eaton CL.