chore: upgrade to Rust 1.90 (#4124)

Inspired by Dependabot's attempt to do this:
https://github.com/openai/codex/pull/4029

The new version of Clippy found some unused structs that are removed in
this PR.

Though nothing stood out to me in the Release Notes in terms of things
we should start to take advantage of:
https://blog.rust-lang.org/2025/09/18/Rust-1.90.0/.

.github/workflows/rust-ci.yml

@@ -57,7 +57,7 @@ jobs:
         working-directory: codex-rs
     steps:
       - uses: actions/checkout@v5
-      - uses: dtolnay/rust-toolchain@1.89
+      - uses: dtolnay/rust-toolchain@1.90
         with:
           components: rustfmt
       - name: cargo fmt
@@ -75,7 +75,7 @@ jobs:
         working-directory: codex-rs
     steps:
       - uses: actions/checkout@v5
-      - uses: dtolnay/rust-toolchain@1.89
+      - uses: dtolnay/rust-toolchain@1.90
       - uses: taiki-e/install-action@0c5db7f7f897c03b771660e91d065338615679f4 # v2
         with:
           tool: cargo-shear
@@ -143,7 +143,7 @@ jobs:
 
     steps:
       - uses: actions/checkout@v5
-      - uses: dtolnay/rust-toolchain@1.89
+      - uses: dtolnay/rust-toolchain@1.90
         with:
           targets: ${{ matrix.target }}
           components: clippy