I haven't done TypeScript/JavaScript in a while. What's the status of ESLint taking over from TSLint (for both the tool itself and the vscode extensions)?

I think the transition is nearly ironed out, I'd say the only concerns are the edge cases but everyday usage should be fine:

https://github.com/typescript-eslint/typescript-eslint

Haven't ran into too many issues within the last 8 months or so. Only in Spring 2019 was it bad IME.