On another note add more ground vias. Double what you think is already too much. Especially at the CPWG -> Microstrip transition.
Think of the return current on the ground contacts. You want that transition as graceful as possible and if there is no direct path for the return current between the coplanar ground and the bottom ground plane it will be forced to take a detour impacting performance.
HTH
Is the test board microstrip or GCPW ("CPWG")?
The lobing in the S11/21 graphs do look to be a launch issue.
GHz+ will need good gnd via rules. Smaller is better to control LC, and spacing/pitch/amount affects all that. I used the smallest plated dia vias I could get for my test GCPW boards.
Compression ports like the SW Microwave clamps are interesting, they do state option for soldering. I would think the best contact protection for no-solder ports is to use ENIG for pin pad along with a gold pin to keep corrosion from impacting signal, copper the rest of the way.
I would also think the FR4 is just shit for ~6GHz+. Would use Rogers or PTFE at that point.
The SMA compression port shown, the pin is machined to fit into a through-hole round pad? That's interesting, that insertion brings the signal closer to the gnd plane on bottom, it's no longer just FR4 there and needs to be accounted for.
Would be nice to see smith chart.