Looks good
I want something like that with a hot tub under it
Hot tubs are a terrible detriment to any enclosure due to the moisture expelled. I'm not sure what good a pergola would be for a hot tub, but it would almost certainly "pay" in deterioration acceleration. Close to the house isn't great either; an installer whom I considered to be an expert gave me all these warnings for consideration in placement. If you want an awning on one, go with a heavy PVC frame and sunbrella fabric for the least loss from moisture damage.