Are there any programming languages with the same syntax as rust (or similar)?

Gleam is very similar syntactically. Never used it, so can't say anything more about it.

Go zig! It's really awesome

Rust is special regarding references but Kotlin reads similarly.

I take it you're not a fan of the borrow rules?

Would you rather manage your memory yourself, or would you rather use a language with a runtime?

Those are your only 2 remaining options for managing memory if you exclude rust-like reference constraints.

Swift is pretty close. I've been trying it out recently after writing years of Rust and it's been great so far (and pretty much completely eliminates the big tooling complaints I have about Rust...).