Amperage, receptacles, breakers
Sounds a lot like my house before I redid my kitchen. Current code requires at least two 20A circuits in the kitchen, for exactly the reasons you stated. My kitchen used to be almost all on one circuit (except the oven &amp; cooktop).  I also have one 15A circuit that powers: kitchen lights, cooktop hood fan/light, 1/2 the bedroom lights &amp; receptacles and 1/2 the main basement room lights &amp; receptacles. Not unusual at all for the 1950s.
But why, you ask, if so much is crammed on each 15A circuit, is there a 20A circuit with just the one receptacle at the panel? Very simple: Your house, like mine, originally had a fuse box rather than breakers. Or even multiple boxes, using the Rule of Six. I still have mostly fuses, except for a small breaker panel added when I redid my kitchen.
In your case, my hunch is that a previous owner decided to replace the fuse box(es) with a nice big panel. When they did that, the electrician added, at very low cost, a convenience receptacle next to the panel. It is quite likely the electrician added some new circuits somewhere, but didn't bother (because it wasn't a problem at the time) to replace the existing circuits. Any of those old 15A circuits that included 14 AWG wire couldn't be changed to 20A, so even though that would be useful, especially in the kitchen, the existing circuits had to get 15A breakers.
If you have room in the panel, you can wire up new circuits to the kitchen. If you do that, they should be 20A and they must have GFCI, either in the breaker or at the first receptacle in each series.