I have the Lutron Smart Bridge Pro, and the Pico remotes used to work with Home Assistant when I was using the third party Lutron component (https://github.com/upsert/lutron-caseta-pro). When HA added the native lutron_caseta component (https://www.home-assistant.io/integrations/lutron_caseta/), I switched over to that to reduce fragmentation, but it looks like it doesn’t support receiving input from the Pico remotes.
The custom component has always been light years ahead of the native one.