I don't know of a standard for authenticating with Nostr on the web, but it is possible to do using Nostr signing extensions.
NIP-07 provides the signEvent function to web apps, NIP-42 defines an event that is signed by the user to authenticate against a relay. The same type of event, or a similar one, could be used for web authentication as well.
signEventfunction to web apps, NIP-42 defines an event that is signed by the user to authenticate against a relay. The same type of event, or a similar one, could be used for web authentication as well.