I wanted to find a way to perform a search with Alfred for emails in HEY. The issue was when doing a search, in HEY, there didn't seem to be a URL change.
After posting what I wanted on the 37Signals forum, I found that the link I posted actually worked! So apparently there as a page/query you can use.
Here's the working link: app.hey.com/search
So I created a shortcut in Alfred, tested it, and it works perfectly! I'm sure you'll be able to do this in Raycast or similar app.
Now I can search without opening HEY first. Just bring up Alfred, type my search query, and hey presto!