So, you plan to overnight at
Plaza Premium Transit Hotel (airside)?
Should be no problem. You simply explain to the transit security that you will receive your boarding pass at the transit desk.
then after transit security, go to the hotel and overnight.
From there, go to the JAL transfers desk to receive your boarding pass.
Hopefully you don't have checked luggage connecting across your two separate tickets, which would complicate things.
https://www.jal.co.jp/en/inter/airport/tpe/transit/
"If you are transferring to flights departing from Terminal 1, please go down to level 1 from the center of the concourse and take the free Skytrain to Terminal 1. Then please go to the transfers counter at Terminal 1 and present your baggage claim tag and your connecting flight ticket to receive your boarding pass, and proceed to your departure gate."