The thing with notifications is that a lot of apps go so overboard with them that I generally choose to silence them completely. This has totally led to important notifications being unseen for some time, but for the peace it is a price I'm ready to pay. Being able to configure notifications with high granularity is something I still have to discover.
On macOS, in iTerm2, Claude will trigger notifications. I was impressed!
(and also annoyed: I don't like notifications. Then again, I don't have Claude do long things where I can go get a coffee)