In cooling mode, heat pumps work by heating the outside of the garage/house. To do this, the refrigerant has to be warmer than outside temperature. For a given fluid, you get an upper limit temperature like you mention, where efficiency drops to zero. This is because the fluid has a critical point, as you approach critical temperature the achievable enthalpy change in the condenser drops to zero.

Is there fluids that are optimized for more extreme climate on both ends?

For industrial use, there's heat pumps optimized for pretty much any temperature range you can think of. We have one in the lab at work that goes from 40 C to 130 C, another (cascade unit) that goes down to -200 C, etc. But price goes way up and efficiency way down as you increase the range.

Can you please direct me to a supplier for the kind of heat pumps you have in your lab? I've been trying to source a high temperature heat pump for an experiment of mine, and I haven't really found what I am looking for yet. I'd appreciate any leads you could give me.

I'm afraid the high temperature one is a custom built unit, actually for an R&D project of some colleagues of mine that aims to demonstrate the efficiency and reliability for high temperature applications. You can email me to discuss, if you want.

Technically, any standard AC unit is a heat pump, so that doesn’t make a whole lot of sense.

Isn't the refrigeration loop "tuned" for a particular operating range? Like, if I want a heat pump for extracting heat from cold winter air, the operating envelope will be set up differently than for a unit designed to dump heat into hot summer air.

I'm guessing here. I just know that the outside condenser and inside evaporator (in a cooling setup) need to match each other pretty well to avoid damage to the compressor or inefficient operation.

I'm sure there are many parameters to tune, although I don't know the details. But a "heat pump" is just a machine that pumps fluid in a certain way to make one end hot and another end cold. With a traditional AC, the hot end is placed outside and the cold end inside. What the HVAC folks call a "heat pump" is a particular variety that can reconfigure itself to put the hot end inside. If you were so inclined, you could heat a space by taking an AC and turning it backwards so the hot end was inside. (This would be pretty dumb unless you needed to heat stuff up in the summer, since the temperature range it's built for would be all wrong otherwise, but it works.)

I'm sure there are heat pumps that don't cool well when the temperature is too high, but I don't think it's a general property of all of them.

It mostly depends on what refrigerant is used. All heat pumps need to be able to change the phase of the refrigerant, which becomes too hard above or below certain temperatures. You can extend the range by having a higher pressure pump, but that reduces efficiency.

FWIW, our central air struggles above 100F has well. On our hottest days (105 F) it can barely hold 80 F inside.