It sounds like the VPN service running in the background is what’s causing the issue, so you may need to terminate the service before shutting down.
I have never used (and will never use) PIA, but I have used Windscribe, Mullvad, Proton, IVPN (recommended), Surfshark, WeVPN, (not recommended) and Tunnel Bear.
I mention these to say that none gave me slower shutdown issues.
For a tier list or good comparison, check out the video below:
