ci: check for public dependencies

[mladedav]

Motivation

We should not expose dependencies accidentally and we should have a check that lets us know that we need to do a breaking release when we update a public dependency.

Solution

Use the unstable cargo public dependencies.

[mladedav]

This might have to wait for a bit since our current MSRV 1.75 rejects the Cargo.toml since it is not stable while newer (e.g. 1.83.0) cargo just prints warnings that we need to enable the unstable feature but otherwise just ignores the field.