Good question. A queenless and broodless colony will have less imperative to forage so it’s to be expected to see less activity. Also as I suspect they swarmed out maybe three weeks or more ago (by there being no remaining capped brood) the total flying population will be reduced. If there is an unlaying virgin present or your test frame raises queen cells, you will know the score soon enough before the bees dwindle out. You may decide if it is to be another month or more before you get a queen back in lay, rather than wait you are better off uniting the remaining bees to one of your other colonies as by that time they will be getting old.
Nature dictates they will eventually die off at a similar rate they were born, so if the queen was laying at a thousand a day so in due course they will (roughly) die off at a thousand a day. Unfortunately in such cases as this, as you point out, there is no recruitment of young bees to replace them.
Two good points to take from it however. Firstly, quick out of the blocks big colonies can be a handful to keep together - your slow starters that don’t swarm will actually bring you in a decent spring and summer honey crop. The early mega colonies boosted by pollen supplants and constant feeding beloved of YouTube commercial outfits are often used to take splits and nucs for sale, rather than kept at that peak for months on end. The takeaway from that is to consider boosting slower colonies by taking capped frames from the over strong ones, so called balancing colonies within each apiary.
Secondly, the very real impact of swarming and possible cast swarming on the remaining so called parent colony. It is highly vulnerable to replacement queen misadventures, inadequate numbers to forage sufficiently to put on a surplus to survive winter, or simply defend itself against robbing bees or wasps. Many post swarm colonies unassisted by beekeepers simply don’t make it to the next Spring.
Get on top of swarming and the rest follows on. Mostly.