> Typescript is not a compiled language.

Compilation or not isn't a feature of languages but of language implementations, but, yes, the primary TypeScript implementation is compiled.

> It is a "transpiled" language.

Transpilation is a subset of compilation.

It's not compiled to native machine code for the target system, but that doesn't make it not-compiled.

If going with that lax definition and concept wrangling, Python is also a compiled language. Python source code can be compiled and byte code can be cached and then Python runtime can load it.

Just like Typescript compiles the source to Javascript which is then loaded by the V8/Node etc.

And thus programming languages can be only of one type - Compiled.

Being compiled or not isn't a property of the language. It's a property of whether you compile it or not. Pure interpreters can exist. They're not very common for "practical" languages. Parse to AST, then call evaluate(ast). No target language necessary.