Unfortunately I have no pictures to clearly show the cap on our pergola We sold the home last year so taking one now isn’t an option. I’ll try to describe and looking thru the corbels might let you understand the concept.

The 6x6 PT posts are wrapped with 3/4” PVC like you propose. Atop I created a cap using 2x cedar covering ALL the seams. Using a table saw a water-shed bevel was trimmed. The corners slightly overhang the structure. It was attached with adhesive. Hope this is helpful.

Super! How did you attach the top part of the pergola to the post? In these pics it is just sitting on top. Or was the top of your pergola joined to the side of the post and the cap is actually above the pergola top?

The Pergola is constructed ”egg crate style” giving a totally flat top and ceiling. Created by cutting notches into 2x12’s. You can see lag bolts between the corbels - there are two each direction going thru the beams and post with the nut and washer on the inside. Also lag screws at each intersecting joint draw the members together - the heads are painted white so look carefully in order to see them in the second pix. Yes, the cap rests directly atop each post.

FWIW, here is a video of the “Setting” with other views of the Pergola.

https://youtu.be/H5t9G-Gujqw?si=q2P_QJwnu462oIno