regex: small cleanups

Just some small polishing. We also get rid of thread_local in favor of
using regex-automata, mostly just in the name of reducing dependencies.
(We should eventually be able to drop thread_local completely.)

crates/regex/Cargo.toml

@@ -21,4 +21,3 @@ log = "0.4.5"
 regex = "1.8.3"
 regex-automata = { version = "0.3.0" }
 regex-syntax = "0.7.2"
-thread_local = "1.1.7"