If you do work related stuff on your computer, your work should be taking care of the computer. This is why most people get assigned a computer by their places of employment, and are not expected to use their own. The place of work has their own tech team who deal with these types of issues. It's a really bad idea to do work stuff on a home computer because it makes your device much more vulnerable to being snooped on and controlled (for example, your place of employment may gain the ability to remotely wipe your device), and generally if you are in such a pickle then you should just not give them your password.

Again, it could be a software issue. If I complain that my WiFi isn't working, and you take it in to have a look, and your diagnostics say that WiFi works, then without the password you can't do anything at all. If my problem is that Safari runs really slowly and you can't log in, you're not going to be able to fix that.

If your only fix is then to reinstall the operating system and hope for the best, then you've done a terrible job.

In any case, the tech has physical access to your computer, and in the presence of that you should not assume any security from your disk encryption. FDE is good for one loss of control; after that you should assume compromise.