Take the cabinet door to Woodworkers Supply or Woodcraft.

How about a picture taken back a bit farther please?

Can anyone share what type of router bit to use to achieve this same cabinet door detail?

One that matches the detail.

What are you doing?

It appears to me that the profile may not be machined into the door. It may instead be two individual pieces of moulding added between the frame and panel.

This looks like a couple separate pieces. But a roman ogee bit for routers is very similar

I agree that is applied molding, not routed out.