I have a 65P that doesn’t get a lot of playing time.
...I want something not too expensive (which probably rules out TI’s),
...low to medium tension, with a smooth feel (not sticky), and a very short break-in period. (I don’t want to spend months breaking in a set.)
...I’ll be playing mostly with fingers, but occasionally using a pick.
Cobalts are out (sticky)
Define short break in period? There are used flats on Ebay or Reverb... or boil the new (supposedly works).
Bright or muddy isn't mentioned.
I personally can't feel the difference in Low tension.
Roto monel maybe
D'addario chromes (supposedly sound the same new or old) they are brighter sounding.
Don't rule out Fender run of the mill flats (bread & butter)
Labella's are polished and are slick (IMHO), advertised as balanced, it takes a while for the low E to come out of that thunky thing.
Ernie is budget friendly so is Fender.
I have the Jamersonesque medium Labella's on a string through... not factory recommended, but it came that way and it is Deep Talkin'... when that bass goes in for a neck shim the Labella's specifically for string through are going on.
You're on the fence.
My first recommendation is to match the existing nut on the instrument rather than altering the nut.
I'm sort of a medium kind of guy but it's hard to match the nut coming out of the factory because most of that factory stuff is cut for light or sorta light, so to manage my string choices the nut(s) had to be fitted for the medium gauges.
I'm thinking... Ernie Ball or Fender, and the choice for me would be the nickel option, but stainless works too. Unless you want bright and that would be the D'Addario chromes.
Is your P-bass a string through? That narrows it way down to basically (my choice) LaBella with silk wraps on the exposed core at both ends...
BTW when I see a flatwound with fret dents I would change them out. Hence, when I was very active playing 3 to 4 gigs a week a set of strings would rarely go over 2 years, and I tried different options rather than one brand exclusively. I also used 2 or 3 basses per gig as the songs dictated. Sometimes I used half-rounds on the six string boat anchor.
Fender flats were very affordable back then. The Beatle bass wore Labella's .96's as I recall.
I actually broke a string once at the (smooth) brass bridge roller, and that was a bridge through fretless Jazz bass (go figure) and I have no idea why that particular string broke midsong, I use my fingers.
Cheers!