Let's not mix apples and oranges, what the EU is doing is testing the CBDC (digital euro) central bank digital currency, and the stablecoins mentioned are private company tokens that are (allegedly) pegged (backed) to fiat currency. Although both are absolutely centralized in their nature, CBDC will be safer in any case because the central banks (ECB) will stand behind them, while any private stablecoin, apart from the risk of being frozen, can also be banned at any time for any reason that the authorities comes to mind.
In addition, from what was written before about the digital euro, every EU citizen should be limited in the amount he can own, and the figure that was mentioned is 3000 EUR.