But does that mean there is too much rental housing available or not enough, versus owner-occupied housing? If you want rents to be lower, it’s strange to argue against an increase in rentable housing.

Rent has also skyrocketed, so your framing as some trade-off between availability of rent or buy does not seem correct.

All else being equal, do you think JPMC building $1B of new rental property to raise or lower rents?

Depends entirely in the property they use to create those units doesn't it? If they demolish 10,000 low end rental properties to build 1,000 high end properties, the answer seems obvious. Equally obvious, if they could create property out of thin air then more supply lowers prices, but property is finite.

If they could buy 10K on-rental-market units at an average price enough under $100K each to leave room to build luxury housing there, it would make a hell of a lot more sense to just continue to rent them.

Well someone is paying it, or else the prices would come down. The middle and lower class are just being pushed out