gpui: Further docs refinement & moved some reexports into 'private' module (#3935)

This commit mostly fixes invalid URLs in docstrings. It also
encapsulates crates we reexport (serde stuff + linkme) into a public
module named "private" in order to reduce the API surfaced through docs.
Moreover, I fixed up a bunch of crates that were pulling serde_json in
through gpui explicitly instead of using Cargo manifest.

Release Notes:
- N/A

crates/collab_ui/Cargo.toml

@@ -61,6 +61,7 @@ schemars.workspace = true
 postage.workspace = true
 serde.workspace = true
 serde_derive.workspace = true
+serde_json.workspace = true
 time.workspace = true
 smallvec.workspace = true