Does semantic memory search require an OpenAI API key

Only if you use OpenAI embeddings. Codex OAuth covers chat/completions and does not grant embeddings access, so signing in with Codex (OAuth or the Codex CLI login) does not help for semantic memory search. OpenAI embeddings still need a real API key (OPENAI_API_KEY or models.providers.openai.apiKey).
If you don’t set a provider explicitly, OpenClaw auto-selects a provider when it can resolve an API key (auth profiles, models.providers.*.apiKey, or env vars). It prefers OpenAI if an OpenAI key resolves, otherwise Gemini if a Gemini key resolves. If neither key is available, memory search stays disabled until you configure it. If you have a local model path configured and present, OpenClaw prefers local.
If you’d rather stay local, set memorySearch.provider = "local" (and optionally memorySearch.fallback = "none"). If you want Gemini embeddings, set memorySearch.provider = "gemini" and provide GEMINI_API_KEY (or memorySearch.remote.apiKey). We support OpenAI, Gemini, or local embedding models - see Memory for the setup details.