Clarification: you waited 30-35 days starting from when?
Typically, if a hive swarms or we make a queenless split, the hive will have no remaining worker brood in 21 days. A queen cell is usually raised from a 1-2 day old larva, emerges in about 11 days, and is mated and laying in another 14. That’s 26 days and another week puts you at 33 - this is the limit: if you don’t have a laying queen you need to take action at this inspection. They’ve already been broodless for almost two weeks, and they haven’t had open brood for about four weeks (open brood has the laying worker inhibitor), so laying workers are already developing. 45 days is well beyond that.
I think the take home message is that you don’t have a big window of time between giving them a mated queen too early and having it killed because they raised a queen and giving them a mated queen too late and having it killed because the hive has laying workers. If you don’t want to roll the dice on the hive successfully requeening itself or worry about this window, get a mated queen in there within a couple days.
Rule of thumb: add queen immediately or wait and check at 28-30 days after the split or swarm. If no laying, give them a frame or two of open brood. This brood will help delay laying workers, and if they are queenless they will start queen cells. Check again 4-7 days later. The queen cells confirm that you need a mated queen asap; it is not generally advisable to let them try to raise a queen a second time.
Joe