A lot of things are possible with Electrum plugins. Since version 4.6, third-party plugins can be distributed as ZIP files, and installed by users at runtime. Maybe #nostr could be used as a plugin distribution channel? Think of a decentralized AppStore powered by web of trust. https://electrum.readthedocs.io/en/latest/plugins.html
That is a good point. Nostr users do not need to be Bitcoin users. Notaries may choose to accept lightning, but also cashu, fiat, shitcoins, or whatever they want. Commercial Nostr portals such as Primal may offer notarization to their paying users, or even to all their users, as long as they find a way to monetize it. In the end, the only thing that matters is whether notarization fees are more economical than the infrastructure cost of a free service that can be abused.