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I'm also having this issue. I upgraded to Big Sur and Parallels 17 around the same time this issue started so either or neither could be the cause...
As an update, I was able to get my bridged network setup working by flipping the net.link.bridge.segmentation setting to 0 as mentioned by Elric...
After upgrading from Catalina to Big Sur (11.5.2), I'm seeing an issue very similar to the original poster (I'm also using Bridged Network mode -...