What did the installers have in mind?

Often the installers don't have anything in particular in mind, their project stops at the door, which might be why the OP is asking.

Carpet is often finished with a minimal metal in various finishes or plastic transition strip that is color matched to the carpet. It might be a cheap look, but it's pretty unobtrusive. If you are keeping carpet in the hall that's probably the cleanest way to finish it.

If the floor were wood you would probably do something wider and more substantial.

https://kofflersales.com/product/carpet-edging-vinyl?itemid=20061&gclid=EAIaIQobChMI5fvP95HvgAMVy0ByCh2v2QkeEAQYASABEgLIS_D_BwE

Yes exactly the contractor didn’t think beyond the tile he was installing…

I was hoping there was something more elegant than the transition strips. We have done wood reducers where we have wood floor in the past, but I guess doing wood (or wood painted white to match tile and door frame?) here would call more attention to it? Ugh.z

We just renovated our bathroom which had a carpet tile interface within the room as well as with adjacent closet. They used some kind of cementitious material to build up a gentle incline under the carpet and peaking at the tile edge.

A threshold is needed, in your case a Hollywood style one. Surprising that the installer did not consider it.

Let me add that the transition between the tile and carpet was basically a butt joint without strips or metal edge. Looked good….

There still needs to be something to capture the edge of the carpet to finish it off, and prevent it from unraveling.

I am a bit confused what flooring was being replaced and why was it not up to the carpet.

Bring in a professional carpet installer prior to doing this. For the carpet, you will need to add a tack strip....the carpet edge will be rolled under and then stretched and tacked to the strip.

Palimpsest the carpet was turned under like they do on carpet used in center of stair.

This should have had a RENO-U under the tile. If you can undercut the mortar with a multi tool, you may be able to slip it in.

If you have enough material you turn under the edge. There is nothing to turn under here; it's already a little deficient.