Please follow this guide when creating a new issue. This speeds up the process of replicating the issue and finding a solution.
The Toggl extension options screen should have a list of available third-party web sites supported by Toggl button.
The list of supported third-party apps is empty.
Go to Toggl button extension settings from Chrome extensions page.
This does not work on the Windows version of Chrome as well.

I was able to replicate the issue. For me the issue happened when I was not logged in. I closed the settings and logged in from the popup and then reopened the settings and everything was fine. List was filled with urls of different tools.
I can confirm that the bug persists even after logging out and logging in from the popup. For good measure, I uninstalled and reinstalled the extension as well, but to no avail.
Screenshot:

@soham2008xyz
Can you please check if the developer console shows any errors.
It should open when clicking on the background page link in the extenstions listing page.

When the developer console opens please select Console tab from the top or maybe it's already opened in the bottom as on the screens shot.

Then refresh the developer console (Ctrl+R or cmd+r) and see if any errors appear. If errors appear send them to me so I can try to replicate and fix.
I opened the developer console, it showed a couple of errors (probably unrelated though, I'm on a flaky connection here). Attaching screenshot:

I refreshed the dev console (Ctrl+R) and the errors went away. I went back and opened the Toggl extensio options page, and the bug persists. However, the dev console output is still empty. Screenshot of extension options page:

Thank you for the details it helped when looking for the reason. This will be fixed with next version.
77c19543758fd9e49d7429aea8edfaabe621e817
Most helpful comment
Thank you for the details it helped when looking for the reason. This will be fixed with next version.
77c19543758fd9e49d7429aea8edfaabe621e817