I’ve noticed both at the gym and the Goodwill near me, that the emergency lights stay on all the time. These are all two light LED models. Has anyone seen this or knows why?

The lights do seem a bit dimmer than I’d expect, but maybe it’s just because the overhead lights being on makes them seem dimmer in comparison.

That arrangement offers simpler wiring, yet it provides easy check whether the thing is working: It can not happen, when the power to the branch is accidentally shut down (even by e.g. a breaker trip) and the batteries left completely discharged and the lights not working when actually needed, without being noticed early even by non-electrician staff (who has no clue what the small indicators are for).
And often the emergency light is not only an area illumination, but also an evacuation guide marking, so things needed in the emergency even when the normal power and lights are still working...

 I have an old emergency light/exit sign combo that has the emergency portion on constantly . Something's wrong in the control circuit .

Afik all exit signs here in Australia are always on. They're on during the night and blackouts at least. The emergency lights themselves in my school only come on during a blackout.

 Exit signs here are also always on  . However , there's 2 sets of lights inside . One set is line voltage and the other is battery voltage and only works when the power goes out . (Supposed to anyways!) The one I have was replaced because the battery portion never turns off . The on board charger is constantly in rapid charge mode due to the drain from the low voltage circuit being always energised .

IIRC the newer LED signs usually use the same LED module. The LED modules usually have two inputs, a 120v/277v input for operation on line voltage and a 6v/12v input for operation on battery power. The older incandescent and fluorescent exit signs did have two sets of lights inside though. The battery backed pair of lights was fed from a separate low voltage backup circuit, or from a on board battery pack.

Old incandescent and fluorescent exit signs didn't have a second low voltage set of lights for battery power. Those operated only off line voltage and would go out if power was lost.

Emergency lights are typically low voltage LED or incandescent flood lights, fed from the same low voltage emergency circuit and typically stay off unless the power is off. There are some exceptions, some older systems used 120v lamps and I've see some of those systems stay on regardless. Emergency systems based off emergency ballast supplied fluorescent lights also typically stayed on.