E.g., in the US, PT time zone, on Sunday, November 6, 2022, 2:00:00 am PT, the clock was reset to Sunday, November 6, 2022, 1:00:00 am PT. If I book a plane scheduled to depart on November 6, 2022, 1:30:00 am PT, how can I know whether the plane is scheduled to depart before the clock is reset?
You can usually tell from the flight duration.
Timetables and listings will show a flight duration. If one of the times, departure or arrival, is unambiguous, you can compute the other time by adding or subtracting the flight duration.
This may not work for flights less than an hour within the same timezone, or if the flight direction/speed perfectly follows the DST changeover, but will handle the rest of the cases.
The clock resets on November 6. 2022, 2:00:00 am PDT to 1:00:00 am PST.
You should check the schedule. If it shows 1:30:00am PDT - then it is before the reset. If it shows 1:30:00am PST - then it is after the reset.
In the US there are no areas in the PT timezone that do not observe daylight savings, so this distinction should appear in all the schedules. If it doesn't - you'll need to contact whoever publishes the schedule for clarifications.
There will be very few scheduled flights at that time of the day (or any other scheduled activities, which is the reason the switch is made in the middle of the night); however it happens.
The flight will explicitly specify which time is meant; before or after the switch. I have seen that before, but have no details to show prove.
I have experienced this often, flying late in the day following the "spring forward" change. Every single time, my 2100 hrs departing flight has been "delayed" by one hour.
As the planes fly multi-leg schedules (of non-stop flights), it really doesn't matter what the ticket says, the flight can't miraculously make up the hour on the time change. It's going to depart at 0500 UTC until there's a sufficient ground layover to catch up. The airlines will not post a custom schedule while the hour gets ironed out across the system; customers will expect their 2100 hrs flight departs at that time "all the time". It's possible of course, the airline already made that up earlier in the route, so if the prior leg had favourable headwinds, maybe it got made up already. So one time, it was only delayed 35 minutes.
I have even contacted the airline the day of the flight to ask the flight status. They assured me it's on time, until the display showed it wasn't.
The TL;DR is your 1:30:00 am PT flight will depart at 1:30:00 am PT. Most likely that's before the timeshift, though your flight may be "delayed an hour, until it's 1:30:00 am PT again!
You may have more luck getting precise information from the airline if you have connecting flights, but now it's a multi-factor problem!