While Emacs 29.1 comes with "treesitter" built-in, you still need to manually build and install any treesitter language plugin implementing the actual language specific parser. This can be fiddly and frustrating doing it yourself.
I had a quick success with using this convenience script: https://github.com/casouri/tree-sitter-module/. It provides fully-automated builds for the most popular languages (including typescript, c and c++).
This is how it works for "typescript":
1. Clone the repository: https://github.com/casouri/tree-sitter-module/
2. Install "build-essentials" (providing a c/c++ compiler if you're on Linux).
3. run "./build typescript" from within the repo
4. Copy the resulting shared library from "dist/libtree-sitter-typescript.so" into your "~/.emacs.d/tree-sitter/".
5. Open a random typescript file and try "M-x typescript-ts-mode" which should not give you any error but instead nice syntax highlighting.
You might find there is a treesitter plugin for your language available and it is even supported by "tree-sitter-module" but there is still no major mode, yet. Happened to me for Perl 5.