WebLN, lnurl all work to accomplish this.

Ideal flow would be a browser extension (or a native LN browser) where you'd automatically withdraw your balance and then pay from your balance as needed (clicking and interacting with websites)

Of course, the extension/browser would be connected to your own node so you'd be in custody of your funds the entire time.

Alby tries to do that with allowances and for withdraw you have lnurl-w balance check, Alby could poll this while you're on a website.

In summary, all tools exist to accomplish this today, just need to optimize the UX