fix: update nightly toolchain to 2025-10-01 for clippy_utils compatibility

The clippy_utils update to 8116b23 requires a newer Rust nightly toolchain
than nightly-2025-08-07 due to changes in compiler internals (HIR types,
trait structure changes, new enum variants, etc.).

This updates the toolchain to nightly-2025-10-01 which should be
compatible with the updated clippy_utils version.

Author: addisonbeck

support/lints/rust-toolchain.toml

@@ -1,3 +1,3 @@
 [toolchain]
-channel = "nightly-2025-08-07"
+channel = "nightly-2025-10-01"
 components = ["llvm-tools-preview", "rustc-dev"]