Is it possible to have a google play billing option on the website? Not just on the mobile app.

I don't think so. At least, it didn't use to be possible, as Play purchases are wired directly into Android, and uses aspects of the OS to secure the process of purchase.

There's a web API where we can check the status of things, which we use from the server to validate if someone has a subscription, for instance. But it doesn't let us generate new purchases.

I'm not 100% sure if there might be some alternative way of offering what you're asking, and I don't really want to wade through the Google Play SDK, to look.

There is an entirely separate Google payment system, called Google Pay. I'm not sure how integrated it is with Play though. Last I heard, for instance, you couldn't use a Play Store gift card on Google Pay, and stuff like that. But, again, I'm not real up-to-date.

Google has a lot of APIs, and tends to whimsically deprecate and destroy them every few years (like, say, Daydream VR), which makes the process of being a developer more "exciting" than we might prefer.

Can I ask why you would want this?

Yeah, the Play store gift cards other than credit cards makes it easier for me to pay subscriptions, Its also what I use most of the time so I wondered if its possible.