Primarily I see 2 core issues you are facing,
1. I receive the links for the old site that aren't valid.
2. How can I reset Google Search Console (parameter url, index,...)?
Two points, first, there is no "one click remove all links" method for Google Search. Second, through Google Search Console is a way for you to provide indication to Google about your website. The more specific you are , the better it is. In you case, if you have revamped your web app and old links aren't valid then point the old links to new ones through permanent redirects. If they aren't valid anymore, throw 404 errors. Over a period of time, the errors will start popping up in console, for you to track and make amends are required.
Lastly, by "reset" if you meant start fresh then one possible, crude way could be to delete the property and create new one.