I don't think the issue at hand is a technical challenge. It's merely a sign, imo, that usage has surged due to AI. To your point, this is a solvable scaling problem.
My worry is for the business and how they structure pricing. GitHub is able to provide the free services they do because at some point they did the math on what a typical free tier does before they grow into a paid user. They even did the math on what paid users do, so they know they'll still make money when charging whatever amount.
My hunch is AI is a multiplier on usage numbers, which increases OpEx, which means it's eating into GH's assumptions on margin. They will either need to accept a smaller margin, find other ways to shrink OpEx, or restructure their SKUs. The Spotifies and YouTubes of the world hosting other media formats have it harder than them, but they are able to offset the cost of operation by running ads. Can you imagine having to watch a 20 second ad before you can push?