All prices listed in the Trade Republic app are real-time prices (depending on your Internet connection).
The price quality of stocks, ETFs, and bonds is monitored on the exchange. Spreads (difference between the bid and ask price) are linked to the XETRA reference market, if tradable there.
All prices displayed in your portfolio overview or in the instrument screen of your app are, in principle, bid prices. If you want to buy a security, the ask price is always displayed. If you want to sell a security, the bid price is always displayed.