I think your view is a bit too optimistic/nice in regards to Stripe, for this specific situation.
Payments have nothing to do with LLMs. They are two different businesses. Doing well in one makes Stripe not particularly well suited to do well in the new, other one.
I see this more of an attempt at capturing hype/eyeballs/attention, given that Stripe has been private for a long time, and that the latest valuation is not particularly higher than the one from years ago. It is a company that I really like, but one should question their real business and how likely they are to go public. Owning Openrouter allows them to insert some "story" about the growth potential of the company.
At the end, the retail investor will pay for all the BS, particularly around AI this time - not sure if this acquistion is the case or not, but I suspect it's a possibility.