I am getting a new bike and want to eliminate the bike computer from my bar space. I am wondering if there is any bike camera setup that can be used as an ersatz bike computer sans display. I already have a mph display as my new bike is an ebike, but I want to upload to strava, garmin connect, etc. This would also mean I only need to start my ride on one device paired to my phone rather than multiple.

Is there any bike camera/gps setup that I can use to do this?

None that I am aware of.
You can use a GoPro with GPS active, but it won't upload to Garmin Connect or Strava. Garmin bike computers can be configured to automatically start recording your ride as soon as you hit 6 mph, and of course they have the ability to upload your data.
I use a combination of a GoPro for video and Garmin 1040 for guidance and data. You can combine the two for data overlay on video with software programs like Telemetry Overlay.