Where are the VSCode error logs for extensions?

When I get an extension error I have no way of knowing why the error happens.

You're probably looking for:

cmd-shift-p -> Search Show Logs -> Extension Host

From what I know there are no dedicated logs for extensions. When you are debugging your extension you can write notes to the console. However, when you have problems with an installed extension this won't help. But keep in mind vscode is kinda "web browser", so it has the usual browser developer tools (see Help -> Developer Tools),

which will show you runtime errors (and all the other stuff those tools allow usually, including the entire vscode DOM). That's probably the best option you have in such a scenario.

And for extensions that use previewHTML (or web views) there's a similar goodie, but tailored towards HTML development. Use ctrl/cmd+shift+P to open the command pallet and type "Webview Tools". Select the match to open a similar view like the one described in the first paragraph. But this one is only for the previewHTML content and allows you to debug that! This view is only available when a page containing a web view/previewHTML is active and closes automatically when the web view tab is closed.