Well, as you can see from the statistics in the first post, it can happen with either method. You did nothing wrong. I think the MSI Center method also calls the normal BIOS flash mode as well in the end, similar to M-Flash in the BIOS. I also exclusively flash via M-Flash, because i don't even consider installing MSI Center (i don't like that tool, it can mess with your Windows settings and for a lot of its features, there are different ways to do it better). But in this instance, i don't think the risk is much lower if you use M-Flash.
If you can't wait for customer support because you anticipate it will take too long, then you can either try with an external programming tool which seems pretty successful here, or you can outright buy a new board, have your old board replaced/fixed by MSI and sell the replacement board later. As you may have concluded yourself, the Flash BIOS Button can be quite an important feature. At least it helps to eliminate any worry about a BIOS update. Most MSI Z590 boards have one, and they can also take a 10th gen CPU.