Google news api is deprecated and there is no such publicly published quota regarding its rate limit. So developers need to switch to the best alternatives of google news API one of them is Newsdata.io which offers global coverage, real-time updates, advanced filtering, and free development access—ideal for news analytics and apps.

And in terms of its rate limit :
Free Plan: 30 credits every 15 minutes.
Paid plans: 1800 credits every 15 minutes.