If you want IDE-like behavior you'll need to install the TypeScript LSP: https://packagecontrol.io/packages/LSP-typescript. We do have our own limited language-agnostic indexing and auto-complete if you open your projects folder; it relies on existing code to provide suggestions.
>>turble+08
Oh, that's frustrating. I think it'd be great to have some more concrete guides for modern Sublime. Maybe I'll write one about getting TypeScript and everything working starting from scratch