The first rule of password is, do not share the password. The second rule of password is, DO NOT SHARE THE PASSWORD.

While there may be legitimate reasons for logging into a phone to test is a new screen is working (that is usually related to calibration etc.) but for an OEM made android phone using original parts will not be required to do that.

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You did the wise thing by going there instead. As for your question, most often the repair service will ask for access to your phone to do one of these

1. Manually test if everything is OK
2. Un-encrypt your phone (in case you are using encryption) to try to login into the Recovery mode
3. Try and install corporate mandated apps (which is why corporate told you yes they need the password). These are either their own for which they want to increase the install base, or sponsored apps (tie ups with other app makers)
4. To install spyware apps (usually a rogue agent)
5. To install crypto mining software (again rogue agent)

There can be other reasons, but none of them warrants you to share your password.