I searched around the web and the official answer seems to be no as Samsung doesn’t provide a public API for connection.
I can manually sync my sleep times from the app. But, I would prefer the automated approach and flexibility of the Sleep app.
While I didn’t see anything promising from my quick search, you might be able to try something with Gadgetbridge and a custom entry. I found older posts talking about it, but I didn’t search well enough to see if there’s been progress
I did try bangle.js gadgetbridge from play store and it showed the fit 3 as incompatible.
I think it might still be incompatible (I see a request to add it), but the play store version is a separate app based on the actual app one. The actual app isn’t on the PlayStore
Bummer. Thanks for helping, anyway.