in SSH, it's a two-way handshake, the client ordering the coffee also gets a cert to prove their identity.
In browser land, the client browser doesn't get a cert to prove their identity, it's one-way only.
Certainly TLS supports client certs, browsers(at least some) technically even implement a version, but the UX is SOOOO horrible that nobody uses it. Some people have tried, the only people that have ever seen any success with client side authentication certificates over a web browser are webauthn/passkeys and the US Military(their ID cards have a cert in them).
webauthn/passkeys are not fully baked yet, so time will tell if they will actually be a success, but so far their usage is growing.
I think webauthn/passkeys will be more successful (frankly I think they already have been) because they're not part of TLS. The problem with client certs, and other TLS client auth like TLS-SRP, is that it inherently operates at a different layer than the site itself. This cross-cutting through layers greatly complicates getting the UX right, not just on the browser side (1) but also on the server side (2). Whereas, webauthn is entirely in the application layer, though of course there's also some supporting browser machinery.
(1) = Most browsers defer to the operating system for TLS support, meaning there's not just a layer boundary but a (major) organizational one. A lot of the relevant standards are also stuck in the 1990s and/or focused on narrow uses like the aforementioned U.S. military and so they ossified.
(2) = The granularity of TLS configuration in web servers varies widely among server software and TLS libraries. Requesting client credentials only when needed meant tight, brittle coupling between backend applications and their load balancer configuration, which was also tricky to secure properly.
So true, two-way certs with TLS have crappy implementations everywhere, not just in the browser.
I have 2 problems with webauthn/passkeys:
* You MUST run Javascript, meaning you are executing random code in the browser, which is arguably unsafe. You can do things to make it safer, most of these things nobody does(never run 3rd party code, Subresource Integrity, etc).
* The implementations throughout the stack are not robust. Troubleshooting webauthn/passkey issues is an exercise in wasted time. About the only useful troubleshooting step you can do is delete the user passkey(s) and have them try again, and hope whatever broke doesn't break again.
In browser land, the client browser doesn't get a cert to prove their identity, it's one-way only.
Certainly TLS supports client certs, browsers(at least some) technically even implement a version, but the UX is SOOOO horrible that nobody uses it. Some people have tried, the only people that have ever seen any success with client side authentication certificates over a web browser are webauthn/passkeys and the US Military(their ID cards have a cert in them).
webauthn/passkeys are not fully baked yet, so time will tell if they will actually be a success, but so far their usage is growing.