Use rust-analyzer's flycheck as source of cargo diagnostics (#29779)

Follow-up of https://github.com/zed-industries/zed/pull/29706

Instead of doing `cargo check` manually, use rust-analyzer's flycheck:
at the cost of more sophisticated check command configuration, we keep
much less code in Zed, and get a proper progress report.

User-facing UI does not change except `diagnostics_fetch_command` and
`env` settings removed from the diagnostics settings.

Release Notes:

- N/A

Cargo.lock

@@ -4399,7 +4399,6 @@ name = "diagnostics"
 version = "0.1.0"
 dependencies = [
  "anyhow",
- "cargo_metadata",
  "client",
  "collections",
  "component",
@@ -4409,7 +4408,6 @@ dependencies = [
  "futures 0.3.31",
  "gpui",
  "indoc",
- "itertools 0.14.0",
  "language",
  "linkme",
  "log",
@@ -4421,7 +4419,6 @@ dependencies = [
  "serde",
  "serde_json",
  "settings",
- "smol",
  "text",
  "theme",
  "ui",