TypeScript TSDK
Typically when a project is having issues like the one you are having, it's because the project and vscode are not succinctly using the same typescript package.
Before I explain below, I want to note that you will not get a TypeScript Version in the status-bar unless VS Code has a TypeScript document open, furthermore, the TypeScript document needs to be recognized as being a TypeScript document which can require that you have written some TypeScript in the document. Also, just because the file is open, and its recognized as a TypeScript file doesn't mean VS Code will only give you the TypeScript version in the status-bar. VSCode will give the version of what ever file-type has focus. So if your configuring typescript in your "tsconfig.json file", and you check the typescript version to see a configuration that you changed fixed the problem, your only going to get a version for JSON, because tsconfig.json is a JSON file. To see the typescript version you must change focus to a TypeScript file.
To start, as a best practice, use the following commands, in the order that they have been presented in, to reinstall the latest version of TypeScript.
npm rm typescript
npm i -D typescript@latest
Add typescript.tsdk to your settings.json file
Add the setting bellow to your ./.vscode/settings.json file. Its considered a best practice to add this to your project level settings.json file because the project level settings.json file overrides the global configuration. Its a safe bet that nothing screwy will happen.
// @file ".vscode/settings.json"
{
"typescript.tsdk": "./node_modules/typescript/lib"
}
The code above tells VS Code, and your project to use the TypeScript install that located in the directory that you assign as a dirpath to typescript.tsdk.
After adding the configuration "RESTART VS CODE" by pressing F1 and typing the following: "Developer: Reload Window"
When you see the option with the name I had you type, select it, and the window will reload.
Note: Exiting vscode, and reopening it manually works just as well, but is much slower.
Alternative TSDK Configuration
You don't have to configure the project to use the project's TypeScript package. You could configure VS Code and your Project to use the version you have installed on your machine (or development server, or what have you). To use a system level typescript install, add the following to your settings.json file.
// @file ".vscode/settings.json"
{
"typescript.tsdk": "/usr/local/lib/node_modules/typescript/lib"
}