As a SWE with about 6-7 yrs of experience as a Sr Engineer, how can I create opportunities to work on patents?

I don't know much about patents, but here's my 2 cents:

1. If you're interested in this, definitely bring it up with your manager. I don't think this is a red/yellow flag at all; it's probably a good thing. I'm sure every manager would be very happy if one of their reports got a patent.
2. I don't think patents are necessary for career advancement, and a lot of tech patents in particular are kind of wonky, just patenting ultra-specific things that aren't super useful or ultra-vague things in a more "patent troll" style.

I actually do have a "patent pending" at Meta, but I didn't really do much for it. This was handled almost completely by the lawyers, who drafted up the technology is complicated legal language, and then I just signed some docs along with the 3-4 other engineers on the patent.

My advice here is not to worry about patents -- they are almost never written by the actual engineer, and at a big company, patents are typically designed just as a protective measure against lawsuits.

I would certainly have the conversation with your manager -- perhaps there is a team or individual who has gotten patents that you could learn from? In general, trying to get a patent if there's not an existing culture for it at the company is very, very difficult (and, I'd argue, not really an indication of true technical progress).