Is it valid to feel uncomfortable with questions unrelated to the grading of your performance?
Yes, definitely. Note that "Are there legitimate reasons to ask this question?" and "Is it legitimate to feel uncomfortable with being asked this question?" are completely different questions. You are completely entitled to your feelings, even if they include discomfort at legitimate questions.
I fail to see how this information was relevant for completing the seminar.
People tend to find personal interactions aid collaboration. Even if the content of the personal interaction is not relevant, the mere fact of there being personal interaction is therefore relevant.
From my point of view, it may introduce bias, if the TA dislikes some of the things he hears from an attendee.
Yes. And the degree to which personal interactions help varies from person to person, and from moment to moment even for the same person. While an extrovert may find the questions fun, a shy and/or neuroatypical person may find the questions to be a completely unnecessary and sadistic spoon expense. The question of how to balance this issue with the general usefulness of personal interaction is not a simple one. Creating an environment where people don't feel put on the spot should be a consideration, such as making it opt-in, or giving participants various options. In the case of "where they were born, currently live and what they do in their free time", the TA could have phrased it as "Tell me about yourself, such as where you were born, currently live, or do in your free time". That phrasing would make it seem more like suggestions of what to talk about, rather than a checklist that they have to get through.
I wanted to confront the TA with my concerns and not answer the questions, but I feared that it may have impacted the grading of my performance, so I didn't.
There should be a means of providing anonymous feedback; if there isn't, that's even more of a concern than the personal questions themselves. It's perfectly valid to share your concerns and ask the TA to take them into consideration.
I feel it's unethical to, even indirectly, "force" students answer questions that may put them in an uncomfortable position by using your position of power.
It's not exactly forcing them, it's just making them uncomfortable if they don't want to, and the catch-22 about consent is that it's difficult to ask for consent without making someone who doesn't want to give it uncomfortable.
How could I go about dealing with similar situations in the future?
Look for when you might be dealing with an X Y problem. When someone asks you for Y and you're uncomfortable giving Y, consider whether there's some X that is really what they want. Your TA says "I want you to tell me what you do in your spare time" and you hear "I need to say what I do in my spare time". But the TA's ultimate goal isn't to collect dossiers on what the students do in their space time (probably), it's to have personal interactions. Asking what people do is a means, not an end. What they're really saying when they say "I want you to tell me what you do in your spare time" is "I want to have a personal interaction with you". So have a personal interaction with them. Tell them what your favorite subject is. Tell them your pronouns. Tell them about your pets. If you spend several minutes talking about yourself, is the TA going to pipe up at the end and say "Hey, you never told me what you do in your spare time"? Possibly. But quite likely not. If they do, they're showing they're prioritizing sticking to a formula over teaching the actual people they have as students.