Quote Quoting Woodsman576
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It just so happens, I'm a male, she's a partially-out lesbian, and my office is an lgbtq+ safe zone, so we sent a lot of time discussing her family issues re her orientation. She told them I'm a father figure to her (I'm so old).
There's where you made your mistake. You have no business getting involved in your employees' personal lives, especially those of a sexual nature. Apparently your employer took serious issue with your behavior.

Quote Quoting Woodsman576
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In the meantime, I've been locked out of my office and banned from any activity within the organization. They still have my personally owned computer, not used for employer activities (I use the organizational computer for that). But since I often worked up to 16 hours a day or longer, I kept my personal computer there for personal stuff. They also have medications, though I can replace those with some cost. They refuse to give me anything from my office, including the computer and meds. Do I have any legal recourse?
Had to read that twice to realize that it was your employer locking you out of your office (terminating your employment), not the state agency taking your stuff.

Your legal recourse is, of course, a lawsuit for the return of your property or for its monetary value.

I don't see you getting anywhere just writing a letter on your own. A lawyer can make one look very scary. Or you can just file suit in magistrate court.