Are embedded congressional districts illegal?

[It’s so Joever]

They should be illegal, I know that much.

Ridiculous, suburbs are different from the city proper.
Nonsense. It's not incredibly common, but there are definitely scenarios where embedded districts can be the most fair outcome. Jacksonville is a good example.

It's not the case in Jacksonville, nor anywhere else. A donut is not a community of interest.

it can be.  The suburbs of a city can absoletely be a COI.

Not by any...seriously defined CoI metric. Suburbs share a COI with the city itself, barring extreme circumstances.