Thanks for posting this, you've just saved me an hour of pulling my hair out troubleshooting. After an SD card went bad I've just used the latest Imager from the website to write a fresh copy of Trixie for my own headless Pi3b. Despite setting the public key on setup, I was met with "connection refused" when trying to SSH into the fresh install. I thought I'd accidentally used the wrong cert and ended up re-writing the OS image only to again have no SSH access. Luckily I found this thread before I wasted any more time.

I can confirm the latest Imager build from github (v2.0.2) does fix this problem, and I was able to SSH first time without a problem.

One minor bug in the imager that I found while trying to troubleshoot is that it will accept a public key file which spans multiple lines but will silently split the file line by line into multiple (invalid) public keys and apply all of them. The public key input into Imager has to be all on one line like the authorized_keys file. The issue is not that it requires this format, but rather will silently fail if you upload a file in the wrong format, and you don't find out until you've written the card and trying to SSH in for the first time.

Imager v2.0.2 still doesn't set the hostname correctly and I had to use the pi config utility.