I know next to nothing, so I watched a youtube video explaining the steps of how a gas furnace works.

https://www.youtube.com/watch?v=tVLtJwix-_8&t=185s

Mine seems to be spending an extended period of time where the inducer fan is running before the pressure switch closes. It used to spend like like 10-15 seconds in that step, but starting earlier today, now might run for a minute or so, before the igniter lights things up. According to the video, that inducer fan will run until the pressure switch activates, which happens when there's enough airflow in the heat exchanger.

If the system is spending a long time running the inducer fan before the switch closes, is that likely to be just a bad pressure switch, or something else affecting the actual pressure/airflow in there?

It can be a bunch of stuff
1) nipple is plugged where the rubber air tube connects
2) leaking rubber air tube
3)lazy air pressure switch, stiff, or hole in diaphragm.
4) slow turning venter motor
5) dirty venter motor wheel
6) heat exchanger crack or obstruction
7)blocked vent.

I usually hook up a manometer and see what the signal is compared to the switch setting and work from there.

Thank you!