feat(server): API relay gateway backend M0-M4

Gin + GORM + pure-Go SQLite. Users/auth (JWT), API key management with
quotas, proxy gateway with weighted channel failover and health checks,
usage/billing ledger, cross-protocol conversion (Anthropic Messages /
OpenAI Chat Completions / OpenAI Responses), and channel/model admin API.
Channels declare native API formats and auto-convert the rest.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

server/internal/pkg/rand/rand.go

@@ -0,0 +1,21 @@
+package rand
+
+import (
+	crand "crypto/rand"
+	"math/big"
+)
+
+const base62 = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"
+
+// Base62 returns a cryptographically random base62 string of length n.
+func Base62(n int) (string, error) {
+	out := make([]byte, n)
+	for i := range out {
+		idx, err := crand.Int(crand.Reader, big.NewInt(int64(len(base62))))
+		if err != nil {
+			return "", err
+		}
+		out[i] = base62[idx.Int64()]
+	}
+	return string(out), nil
+}