You transport the solar gains throughout the house via an operating heating system; if it's off, then not. The room overheats because of the solar gains and not because of the underfloor heating. Turning off the heat pump doesn't help at all in that case.
If the sun only falls on the floor, that might even be true, but I don't assume that.
If, on the other hand, the sun falls on walls or furniture, kitchen countertops, etc., the room would have to overheat through the supply temperature to transport heat via the underfloor heating. So that's rather nonsense.
And regarding people: while I work, I contribute 100W as a person, plus the computer and monitors.
So 300W of heating power. The underfloor heating also provides that. So if I'm not in the room, I need the underfloor heating; if I am in the room, I definitely don't need it.