Which repo were they referring to that was growing too big vertically?

The biggest very active repo I know of is nixpkgs, and I heard it was a stress test for GitHub already.

Possibly this dude's repos? https://github.com/xesf

Every day, he sends hundreds of commits to his (most likely vibecoded) repositories of retro games recompilation.

Possibly Shopify's monolith.

Or alternatively someone is doing something very silly.

Nah, they replaced GitHub with some in-house videcoded stuff a few months ago, and from what I hear from the grapevine it's not going well.

But there's a number of other big private repos with a high rate of merge on GitHub, and indeed it's currently a bit painful, e.g. the subroutine that check whether a PR can be merged tend to take ages. So my read is that they want to better support these big customers out of concern that they might leave too.