Unfortunately, this is a fairly difficult task. In my experience, even SOTA models like Nano Banana usually make little to no meaningful improvement to the image when given this kind of request.

You might be better off using a dedicated upscaler instead, since many of them naturally produce sharper images when adding details back in - especially some of the GAN-based ones.

If you’re looking for a more hands-off approach, it looks like Fal.ai provides access to the Topaz upscalers:

https://fal.ai/models/fal-ai/topaz/upscale/image

Seconding the Topaz recommendation. Although be aware that is the Image upscaler model, and the parent commenter asked about video.

Here's the Fal-hosted video endpoint: https://fal.ai/models/fal-ai/topaz/upscale/video

They also offer (multiple; confusing product lineup!) interactive apps for upscaling video on their own website - Topaz Video and Astra. And maybe more, who knows.

I have access to the interactive apps, and there are a lot of knobs that aren't exposed in the Fal API.

edit: lol I found a third offering on the Topaz site for this, "Video upscale" within the Express app. I have no idea which is the best, despite apparently having a subscription to all of them.