Lake union I would never swim in, because of the major reasons you called out. It’s heavily trafficked by planes and boats, and a lot of the boats don’t care, or their rich people who are not paying full attention. I’ve seen people SUPing in there, at least you’re more visible i guess. Idk if it’s right by like, their dock they own then fine, because no one should be coming in, but I would never venture out very far. Way way way too busy of a waterway.
Alki Beach and Golden Gardens is where I’d go if you want to get in the water. I haven’t heard any bacterial issues here in WA, but maybe do a news search on it? Those areas everyone expects people to be in the water and boats don’t go near.