The EU issuing bonds is technically, illegal. Something like ECB underwritten Corona bonds would be a direct violation of the treaties that make up the EU. Under the treaty that created the ECB, the Maastricht treaty, the ECB is not allowed to fund governments. Each individual government must fund themselves. This was considered the appropriate way to setup central banks at the time. By in large each central bank had rules like this at the time. Now it is considered a rather quaint idea from a simpler time.
In 2012 or so, the interpretation of the definition of not allowed to fund governments was fudged. The treaty was interpreted rather than not allowed to fund governments, it became in general not allowed to fund governments. Draghi spent a lot of effort building support for that fudge. Once he got support from all stakeholders he then held a famous press conference in which he said that the ECB would do what ever it takes.
The courts have played ball. So long as most of the money governments borrow comes from the primary markets, constitutional courts have decided to go along with the fudge. The German courts are the problem. They have put a number on the fudge. The ECB can fund up to a third of a government’s borrowing requirements. Any more than that and it is pushing the law from a fudge into too illegal territory.
The type of money being talked about would push the ECB funding of governments way way past the values the courts were willing to overlook.
Will there be Corona bonds underwritten by the ECB? I’m guessing yes. I suspect though that it will take time. Politicians will need to come up with a way of moving from a fudge into the territory of just ignoring what the constitution says. I’ve no idea how this will be done or how long it will take.