Teacher availability links and calendar feeds
Collect each teacher availability with a private link, and give them a calendar feed of their lessons.
Send each teacher a private availability link. They fill in their own times in a simple form, with no login needed.
Each teacher also gets a personal calendar feed. They subscribe once, and their lessons show up in their own calendar app and stay in sync as the schedule changes.
Availability links and calendar feeds are private to each teacher. Share them directly with that teacher.