i cannot find where on my new-to-me desktop pc to sign in to my Firefox browser.

If I ask a question, does Firefox or Mozilla expose my email address?

If I ask a question, does Firefox or Mozilla expose my email address?

No, unless you deliberately spell it out in your question text, use it as a display name or other profile metadata, or part of the username (neither seems to be your case).

You can check the help articles:

• How do I set up Sync on my computer?
• How to perform Sync on Firefox desktop

that will show you the entry points. It's in Settings, in the browser main menu, in the default "account" toolbar button and many more — at least some of these should be prominently visibly in a fresh installation right away.