AWS AppRunner is the closest equivalent to Cloud Run. Its really not close though, AppRunner is an unloved service at AWS and is missing a lot of the features that make Cloud Run nice.
I agree with the unloved part. It was a great middle ground between Lambda and Fargate (zero cold start, reasonable pricing), but has seemingly been in maintenance mode for quite a while now. Really sad to see.
AppRunner was Amazon's answer to AppEngine a full decade+ later. Cloud Run is miles ahead.