Can't find Slack app on Apple Watch

Check the App Store for your country and see if the app is still available. It is possible it is no longer available for your location.

Looking in the US App Store, I do not see it when searching from the Watch app. IF I go to the App Store app on the phone, it appears, but does not show that it supports the Apple Watch. It is listed as a business communication app. Is that correct?

Try restarting both the phone and the watch. I've had a bit of trouble lately where apps don't show up as available to install on the Watch until I restart things.

Is it possible you were just getting notifications before? I GroupMe, a group messaging app. It doesn't have a Watch app but the notifications appear on my watch and I can respond to them. In the Watch app, go to Notifications and make sure you have them enabled for Slack.

It is possible. However, I would follow Idris' recommendation to start with. Otherwise, you may have to contact the app developer to check, since as I said I only see an app available for the iPhone and iPad. No watch support shown.