I don't know about what other strictness you're referring to but exhaustive enum matching is common check in most TS stacks via eslint. Yea, it's not builtin, just saying there's a solution and it's super common.

last time I researched enums in TS for a project, they were a mess such that it was better not to use enums in the first place

You can actually have it built-in (via default case in 'switch' statements having a 'never()' statement). But it's less powerful than Rust's.