From cut-in to cut-off, maybe finishing a toilet fill, it takes 30 seconds. Is that normal?
Thirty seconds to refill the pressure tank is not usual and not recommended.
As mentioned above, to reduce the frequency of pump cycling, the minimum recommended running time to refill a pressure tank is 60-seconds, but 120-seconds run time is preferable to further reduce cycling frequency. To obtain 120-seconds minimum run time with your existing pump, would require an 80 gallon tank which will provide approx 20 gallons drawdown capacity.
Instead of incurring the substantial additional expense for a much larger pressure tank which will also consume additional space, you could instead install a CSV. Because a CSV will prevent the pump from cycling whenever the pump is operating and more than 1gpm is being consumed, a large pressure tank is no longer needed. Although a CSV and a 5 gallon tank is quite sufficient for most single family residence applications, you could continue to utilize your existing 20-gallon tank with a CSV if desired.
A CSV will fill 1/2 of the pressure tank's drawdown capacity while at the same time supplying constant pressure to house fixtures. Your existing 20-gallon PT will then be 1/2 filled with ~2.5 gallons water. Once no further water is being consumed, the CSV will permit the pump to supply only 1 GPM to fill the tank's remaining ~2.5 gallon drawdown capacity. With ~5 gallons now within the tank, the pressure will have risen to the pressure switch cut-out pressure, causing the pressure switch to shut off the pump.