Following some advice from @stephack in this post many months back, I just updated my blueprint in the first post to comment out the ‘integration’ line below.
selector:
device:
#integration: lutron_caseta
model: PJ2-2B-GXX-X01 (Pico2Button)
Let me know if that solves the issue or not.
I am not currently using any Pico remotes directly with Home Assistant, which is why I have not been on top of any of these issues over the past few months.