I’d like to think of it as the fusion of the evershrinking rational parts of the existing parties who want to get mutually advantageous things done in a productive, constructive way. We can happily ditch the extreme Left and fascist, religious and libertarian Rights.
That's the main point, "center" is synonymous of status quo in politics. So we get more neoliberalism from it. Macron and Starmer are both in that vibe. Once in power they take ideas from the far right, because it's much more compatible with preserving the assets of the ones who put them there.
It's mostly discarding the insane ideas of both the Democrats and Republicans. What's left isn't sexy or cutting edge, but it's probably better policies than the more extreme platforms...