Does a repair shop need my iPad password to test it after battery and charging port replacement?

This Apple article:

Prepare your iPhone or iPad for service - Apple Support

describes what you should have done before taking it in. If you did not then the service people cannot test their work. It's up to you to decide how to proceed now. Is the service provider local? Of so, you may be able to go there and enter the password yourself so they can continue.

I feel the service provider should have told you this when you dropped it off. Make sure the provider knows what they are doing.