well no storage can be 100% efficient but you are correct that thermal storage is very efficient if you want a thermal gradient to leverage for heating (cooling as well)

If I have a room, and I want it hotter than outside now, and hotter than outside later, then putting an insulated box in the room and heating the stuff inside the box, then adjusting the lid to heat the room at the rate I want is 100% efficient. There is no loss eitber in practice or in principle nor any mechanism for one. This is true so long as I want all of the heat, even if I stored high grade heat and run it through a heat engine to make work before heating the room with low grade heat (in which case I might even call it a coefficient of performance of 1.3 or “130%”). I will never match the COP of a similarly engineered heat pump if all I want is low grade though, so in this sense “efficiency” is <100%.

Carnot batteries (where I have a box but don’t want heat now or later but do want work) are quite inefficient (10-50% + a time based loss that only becomes negligible at the GWh scale) , or thermal storage in unheated environments (time based loss) are much less efficient.

A separate heat and cold store from a heat pump feeding a combined heat and power generator is another variation (where a COP might come close to or exceed 1).

F=ma is a bit of a thought terminating cliche (as well as being poor communication and missing a term). E=Fh=mgh. As per my link there are plenty of suitable hills and gullies over about 90% of where people live. A human made structure to lift will always be questionable.

I guess it depends on what you mean by rare long duration events but yes one can imagine a situation where the burning of hydrogen is justified on an energy needs basis

A handful of hours of storage (3-12) can pretty trivially meet loads 90-99% of the time. The remainder tends to be events that are 50-200 hours. Pumped hydro and non-round-trip storage (such as delaying EV charging, overprovisioning an industrial drying step and running it when electricity is cheap, direct ammonia electrolysis for fertiliser during high production times, or storing domestic heat in a pond for winter) can cover most of these.

For the remainder (odd once-in-a-decade weather events or major infrastructure failures) the duration is even longer (100-1000 hours). One strategy is to just keep fossil gas generators around because 100 million tonnes of CO2 emitted and 1100 tonnes of CO2 removed that month may be easier than 0 and 1000. Another is to make something with electricity to burn (which could involve an electrolyser and could involve hydrogen gas storage but does not have to).