Those things exist, and they work pretty good. I don't know if they have a single receiver or a separate receiver for each antenna. Examples:

http://www.jrc.co.jp/eng/product/lineup/jlr21_31/pdf/JLR-21....

https://comnav.com/wp-content/uploads/2018/10/WEB_GNSS-G2G2B...

A traditional gyrocompass is the more common option though, I think.

A purpose-made device that estimates orientation by measuring the phase shift in the GPS carrier waves would be pretty cool. GPS receivers synchronize their internal clocks to GPS time within nanoseconds anyway, though, so it seems like getting raw timing data from two receivers and processing them together is still pretty good and doable without having to DIY a GPS receiver.

Well this is just how GPS works. Each satellite broadcasts what time it is and you calculate your position by knowing the orbit of each satellite and the varying delays in “now” timing received from a few satellites because of the speed of light and a few higher order effects.

That can get you xyzt position, if you want your three dof direction too, a second receiver/fe/antenna can do a second fix and the differential between the two can be used to find the orientation.

You can do this with a smaller antenna separation better by going down the stack into the guts of the receiver math but it’s difficult because these things are implemented in hardware and encumbered by arms control regulatory hurdles.

same general concept as antenna alignment tools used by tower climbing contractors. It has both magnetic compasses and several GPS receivers in it.

https://www.viavisolutions.com/en-us/products/3z-rf-vision