fix: correct all documentation inaccuracies about cookie-based auth

- Fix false claim 'clients never need to handle the token directly' —
  CLI clients (curl, custom HTTP clients) must explicitly manage cookies
- Replace 'token' with 'cookie' in multi-client diagram (token_a → cookie_a)
- Fix Set-Cookie placeholders in protocol diagrams (<token> → <random_hex>/<cookie_a>/<cookie_b>)
- Fix 'old token' → 'old auth cookie' in QUIT command description
- Fix 'get token' → 'get auth cookie' in Client Development Guide
- Fix 'Tokens are hashed' → 'Cookie values are hashed' in Security Model
- Fix 'client tokens are deleted' → 'client auth cookies are invalidated'
- Fix 'Cookie sent automatically' → 'Cookie must be sent' in diagram
- Fix 'eliminates token management from client code entirely' rationale
- Fix 'No token appears in the JSON body' → 'No auth credential appears'
- Fix 'encoded in the token' → 'encoded in the cookie value'
- Fix 'Clients never handle tokens directly' in JWT comparison section
- Update clients table token column description for clarity
- All remaining 'token' refs verified as legitimate (pow_token/hashcash/JWT comparison/DB schema column name)

internal/handlers/api.go

@@ -335,7 +335,7 @@ func (hdlr *Handlers) executeCreateSession(
 
 	hdlr.respondJSON(writer, request, map[string]any{
 		"id":   sessionID,
-		"nick": payload.Nick,
+		"nick": nick,
 	}, http.StatusCreated)
 }