After verifying the repo picker appears for cloud sessions on the welcome page (the fix for #290511 by @DonJayamanne), I experienced a separate issue: a previous unrelated different cloud session from 6 months ago was opened in my VS Code after delegation:
The new correct session + PR would've been bamurtaugh/devcontainers.github.io#61 (which was just generated).
I believe we discussed this is due to #289345, but per @DonJayamanne's recommendation, I'm filing an issue just in case we want to track it separately.