Have a look at Debian Edu to see if it meets your requirements.
https://wiki.debian.org/DebianEdu/Documentation/Bullseye/AllInOne
- Central management is covered by the GOsa Web UI
- Locked down accounts/Wipe session on logout: Not seeing anything in Debian Edu's docs about Kiosk mode but the XFCE desktop does support Kiosk type functionality - https://wiki.xfce.org/howto/kiosk_mode
- Pushing an installation could be done via PXE
Ask on the mailing list(use this) or irc channel if anyone can share their setup:
https://wiki.debian.org/DebianEdu/Documentation/Bullseye/AllInOne#DebianEdu.2FDocumentation.2FBullseye.2FSupport.Volunteer_based_support