This proposal (affectionately known as SHADOW) is an alternative to EIP-1193 for wallet discovery in web browsers that requires no special permissions. Web pages intending to open a connection to a wallet inject an iframe tag pointing at a well-known scheme. Communication between the page and the wallet uses the postMessage API.
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The proposal pull request: Add EIP: Scheme-Handler Discovery Option for Wallets by SamWilsn · Pull Request #7039 · ethereum/EIPs · GitHub
Some WebExtensions to show a proof of concept: GitHub - SamWilsn/wallet-demo
These show an extension replying to a postMessage using an iframe and protocol handler in both Chrome and Firefox.