That looks expensive and I can't underdand what it's supposed to do.
Pergolas are best used to support plants all year round.
For hot tubs a sunshade, for the few weeks a year it'll be used durfng the daytime when it's very sunny.
The OP asked for Pergolas... sure some smaller ones are used for plants but the majority are not. They are a compromise that allows some shade some sun, and good air flow. You can buy ready-made smaller pergolas for hot tubs exactly like he was asking about... or you can fab one up on your own. Depends on skills and tools.