nix: Use flake-parts, partitions, and treefmt-nix (#45321)

Release Notes:

Refactored:
- Use [flake-parts](https://flake.parts/index.html) modules
- `nix/shell.nix` -> `nix/modules/devshells.nix`

Added:
- Use
[flake-parts.partitions](https://flake.parts/options/flake-parts-partitions.html)
to isolate dev dependencies so that flakes that use `zed-editor` don't
fetch dev-only inputs such as `treefmt-nix`
- [treefmt-nix](https://github.com/numtide/treefmt-nix)
  - nixfmt
  - rustfmt

Fixed:
- `shell.nix` and `default.nix` fetching `flake-compat` from
`flake.lock` which added an extra and unnecessary input/dependency to
`flake.nix`. Fixed by setting a fixed rev and sha256 instead.
- `nixfmt-rfc-style` is deprecated and is now `nixfmt`
- Fixes #45338 by using rust-overlay toolchain directly
  - Previously, the devShell included `rustup` which caused slow startup
times as Nix would build rustup from source (including running its test
suite). Additionally, rust tooling (cargo, rustfmt, clippy,
rust-analyzer) wasn't available in the dev shell.
- cargo, rustc, and rust-toolchain.toml components included in
`rustToolchain`

Chore:
- Update `flake.lock`
- Format Rust code with `rustfmt` via `treefmt-nix`

---------

Co-authored-by: Jakub Konka <kubkon@jakubkonka.com>

shell.nix

@@ -1,11 +1,10 @@
 (import (
   let
-    lock = builtins.fromJSON (builtins.readFile ./flake.lock);
+    rev = "v1.1.0";
+    sha256 = "sha256:19d2z6xsvpxm184m41qrpi1bplilwipgnzv9jy17fgw421785q1m";
   in
   fetchTarball {
-    url =
-      lock.nodes.flake-compat.locked.url
-        or "https://github.com/edolstra/flake-compat/archive/${lock.nodes.flake-compat.locked.rev}.tar.gz";
-    sha256 = lock.nodes.flake-compat.locked.narHash;
+    inherit sha256;
+    url = "https://github.com/NixOS/flake-compat/archive/${rev}.tar.gz";
   }
 ) { src = ./.; }).shellNix