refactor(types): migrate from tsd to tstyche

[Puppo]

Summary

• migrate type tests from tsd to tstyche
• rename the type test file to .tst.ts and update assertions to the tstyche API
• remove the dedicated tsd config and update package scripts/dependencies
• move type test files from test/types/ to types/ for a clearer project structure
• move type definitions from root to types folder

Test plan

• Run npm run typescript
• Run npm test

[mrazauskas]

lgtm