How do web browsers work with multiple NICs?

If I have 2 or more NICs on the same computer, both connected to stuff... and I open a web browser, how does it know which NIC to use?

I generally understand layer 2 switching.. generally understand ARP... generally understand you need to avoid conflicts. Is the browser going to do its regular TCP protocol thing to figure out which NIC can get to that address? ...and it'll just ultimately work as long as there aren't conflicts?

Are there any drawbacks from the browser perspective of things? What if I had only 1 device on each network other than that NIC.... So one NIC touches 1.1.1.1 and the other NIC touches 1.1.1.2, and I just go to one or the other address repeatedly.. is the browser going to have no problem with this? (I understand if you ever have the same IP, it'll be a conflict and not work correctly).

I have computers with two NICs, one going to the internet and one going to a bunch of cameras. Sometimes I'll type in a camera IP, it doesn't find it fast enough, so BING will show me a result for that IP, which isn't what I wanted. I'm guessing it's just because the camera doesn't respond fast enough so it went with the other NIC.

Thank you