feat(cli): enrich user-agent header for client requests (#21483)

Adds the following information to CLI User-Agent headers to aid
deployment administrators in troubleshooting where requests are coming
from.

Before: `Go-http-client/1.1`
After: `coder-cli/v2.34.5 (linux/amd64; coder whoami)`

🤖 These changes were generated by Claude Sonnet 4.5 but reviewed and
edited manually by me.

cli/root.go

@@ -684,6 +684,7 @@ func (r *RootCmd) HeaderTransport(ctx context.Context, serverURL *url.URL) (*cod
 func (r *RootCmd) createHTTPClient(ctx context.Context, serverURL *url.URL, inv *serpent.Invocation) (*http.Client, error) {
 	transport := http.DefaultTransport
 	transport = wrapTransportWithTelemetryHeader(transport, inv)
+	transport = wrapTransportWithUserAgentHeader(transport, inv)
 	if !r.noVersionCheck {
 		transport = wrapTransportWithVersionMismatchCheck(transport, inv, buildinfo.Version(), func(ctx context.Context) (codersdk.BuildInfoResponse, error) {
 			// Create a new client without any wrapped transport
@@ -1497,6 +1498,22 @@ func wrapTransportWithTelemetryHeader(transport http.RoundTripper, inv *serpent.
 	})
 }
 
+// wrapTransportWithUserAgentHeader sets a User-Agent header for all CLI requests
+// that includes the CLI version, os/arch, and the specific command being run.
+func wrapTransportWithUserAgentHeader(transport http.RoundTripper, inv *serpent.Invocation) http.RoundTripper {
+	var (
+		userAgent string
+		once      sync.Once
+	)
+	return roundTripper(func(req *http.Request) (*http.Response, error) {
+		once.Do(func() {
+			userAgent = fmt.Sprintf("coder-cli/%s (%s/%s; %s)", buildinfo.Version(), runtime.GOOS, runtime.GOARCH, inv.Command.FullName())
+		})
+		req.Header.Set("User-Agent", userAgent)
+		return transport.RoundTrip(req)
+	})
+}
+
 type roundTripper func(req *http.Request) (*http.Response, error)
 
 func (r roundTripper) RoundTrip(req *http.Request) (*http.Response, error) {