re: What kind of hand saw for this job?

Firstly; amazing pergola. I’m not a huge fan of pergolas (most look kind of clunky and a cheap version of Japanese architecture) but this design looks great. May have to copy it some day.

About the tenons; These are going to be big, fat tenons and it’ll be hard to get them fine woodworking level of perfect. I’d clamp a board to the brace as a guide and use a circular saw to define the shoulders and cheeks of the tenons. This should get you pretty close and and remaining wood would be easy to cut using the circular saw cuts as guides.