Copilot flows and adaptive card dynamic binding

We are encountering challenges with dynamically binding an adaptive card in the Copilot bot with calendly type experience with an option for user to choose the dates and the respective slots based on the date selected. We are passing the input from a JSON response which is generated from Power Automate flows.
Few challenges to note:
Not able to bind dynamic ones with json "${}"
Not able to view the right output with the formula while we do a filter/distinct to find unique values and to filter slots based on the date selection.
We are able to do it with static content however facing difficulties while working with dynamic binding. Attached, you will find a sample adaptive card formula along with a JSON sample from the Power Automate response for your review. Any assistance in this matter would be greatly appreciated. Thank you in advance!

sample json:
sjon sample.txt
adaptive 1.txt

Start with the attached sjon sample.txt and adaptive 1.txt files, reproducing the dynamic binding and filter/distinct behavior described in the issue. Compare it with the static-content case, then isolate whether the failure is in Power Fx evaluation or the Copilot and Power Automate integration; done means a minimal failing example, expected output, and a confirmed project area.