How to get Google Search to crawl a Chrome extension URL?

My Chrome extension that has been getting 250+ installs every day for the past 2 months still does not appear on Google Search.

It seems I am not the only one experiencing this, and many Chrome extensions that have released in the past 4 months are still not anywhere to be found on Google search,.

I also get tens of thousands of impressions every week, and thousands of page views every week.

This is super annoying considering that's where 50% of the install traffic would be coming from, the only way my users can find my extension is via Chrome Web Store search.

I tried contacting Chrome Web Store one stop support and telling them about this, they replied that they have no control over Google search results.

Since I do not own the Chrome webstore domain, I cannot use Google Search Console URL Inspection tool because you must own the domain to do that.

My question for everyone:

Does anyone know of a way to get your Chrome extension to index on Google search results? Clearly getting lots of installs doesn't make a difference, it has been nearly 3 months.

Any advice would be greatly appreciated.