Can't SSH to agentless nodes from Web UI

[nklaassen]

Expected behavior:
I can SSH to an agentless node from the web UI

Current behavior:
I only see this message in the Web UI:

disconnected
this request can be only executed by a proxy

Using tsh or openssh from the terminal is working.

Bug details:

• Teleport version: 13.0.0-alpha.1 (with use correct certificate extension when getting cluster of agentless node #24909 patched in)
• Recreation steps:
  1. Follow the guide to connect an agentless node
  2. Agentless node is visible in the Web UI servers list
  3. Try to connect with a valid login
• Debug logs: This is logged on the proxy:

2023-04-20T10:59:08-07:00 DEBU [WEB]       Attempting to issue a single-use user certificate with an MFA check. web/terminal.go:500
2023-04-20T10:59:08-07:00 WARN [WEBSOCKET] Unable to stream terminal - failed to dial host. error:[
ERROR REPORT:
Original Error: *trace.AccessDeniedError this request can be only executed by a proxy
Stack Trace:
        github.com/gravitational/teleport/api@v0.0.0/client/client.go:865 github.com/gravitational/teleport/api/client.(*Client).GenerateOpenSSHCert
        github.com/gravitational/teleport/lib/agentless/agentless.go:79 github.com/gravitational/teleport/lib/agentless.createAuthSigner
        github.com/gravitational/teleport/lib/agentless/agentless.go:51 github.com/gravitational/teleport/lib/agentless.SignerFromSSHCertificate.func1
        github.com/gravitational/teleport/lib/proxy/router.go:280 github.com/gravitational/teleport/lib/proxy.(*Router).DialHost
        github.com/gravitational/teleport/lib/web/terminal.go:766 github.com/gravitational/teleport/lib/web.(*TerminalHandler).connectToNode
        github.com/gravitational/teleport/lib/web/terminal.go:679 github.com/gravitational/teleport/lib/web.(*TerminalHandler).connectToHost.func2
        runtime/asm_amd64.s:1598 runtime.goexit
User Message: this request can be only executed by a proxy] session_id:662378d1-b625-46df-8470-c76ec339e486 web/terminal.go:768