Hey Peter,
I’m not an expert on flats, but I’ve tried several kinds, so here’s a summary.
Fender flats - First flats I ever tried. Stiff, thumpy, almost no high end even when new. I wouldn’t recommend them as a first ever flatwound string, but you might like them once you get into the flats world.
Ernie Ball (not Cobalt Slinkys) - Stiff, thumpy, not much high end, but a little more than the Fenders. The set I had was a heavy gauge, so they were definitely stiff & high tension. Would not recommend for a first set of flats.
D’Adderio Chromes - In a light gauge, these are not too stiff and are somewhat flexible. They have significant high end when new, but it starts to mellow out fairly quickly (a few weeks if played regularly). When the high end is gone, they have sort of a “clank” that a lot of players don’t like, but I like it with the tone knob rolled off. I also like them on fretless. I’ve had several different sets of these in different gauges. I’d recommend a light gauge of Chromes, .040-.095”.
Ernie Ball Cobalt Slinky - This is the flat that sounds most like a round wound to me. Very bright for a flat wound, something like 3/4 as bright as a round wound. I know you are looking for a string to go on a Pbass, but EB Cobalt flats seem to be made for a Stingray. I’d recommend the lighter gauge in these.
Thomastik / Infeld Jazz flats (TIJF or TI’s) - you will never see a thread about flats without these coming up. They are very flexible and low tension for a flat wound, but with the right neck relief, they feel fairly normal. I like the feel of these better than most flats, but they aren’t my favorite for tone. I like the tone, but not as well as EB Cobalts. TI’s have a better traditional tone without being as dead sounding as some flats. Some say they have a lot of high end, but EB Cobalts have triple the high end to me. The TI’s have a lot of high mids & took me a while to EQ how I wanted to hear them. I have two sets so far. There’s only one gauge I know of, and they are pretty light. I’m neutral on recommending them to a 1st time flats user, especially if that player doesn’t do their own instrument setup.
good luck.