You don't have to provide bank details. There are many options for trading Fiat and using banks are only some of the options. However, bank services are the most popular options.

For more anonymous methods, a US Money Order, Amazon gift cards or cash in-person.

Even if you decide to use a bank, the bank doesn't know you're using Bisq or even buying BTC. It just appears as a P2P transfer to/from another individual's bank account. Nothing inherently suspicious about that.

Bisq does not collect your bank account info. There is the concept of "account signing" when you want to trade an amount above a certain threshold amount that is required for certain payment methods (e.g., bank transfer). Essentially, it's like a vetting process -- you do a small trade with a seller who is signed, and after that trade completes and time has passed your account will become signed as well. After that, you are permitted to trade higher amounts.

More details here:

But you never send payment to Bisq, only to the seller (your trading counterparty, or "peer")

Of course, the seller will have information from your bank transfer which reveal some of your identity. But the bank doesn't know that the transaction was related to a Bisq trade.

In your example, the bank doesn't know what you are buying, but it will know that you send money to someone.

If they FBI for whatever reason catches that person and gets access to their accounts, then they can see that the person received money from you. If they also get access to their wallet, then they can connect the dots and see that you made a buy from that person.