How to know for stadia base player when discount games arrived in stadia pro ? An update list is existing ?
There is not really a list when new games arrive, neither for Stadia Pro nor for Stadia base (when base will be released). You can just see the current ones.
Guess the only thing you could really do is having an eye on the Stadia App or on stadia.google.com. The Stadia Pro deals for example have an expiry-date, so it's worth to check the Store again after the "old deals" ran out, because often new deals are coming after that (normally).
Bookmark the following URL to check for latest Stadia Pro deals for titles (doesn't display add-on deals though).
https://stadia.google.com/store/list/45
This will display any currently available Stadia Pro Deals, you will however need to select each entry to identify the expiration date for the deal. Any deals that have expired will disappear from the list automatically. If there are no deals currently active, the list will just be empty.
If you wish to see add-on deals then you need to drill down into the game title to see any offers applicable there.
You could also follow Stadia on Twitter @GoogleStadia . They usually post the same announcements that get posted in the forum here.