docs: PZERO OpenAI-compatible chat.base-url example

Please do a quick search on GitHub issues first, the feature you are about to request might have already been requested.

Expected Behavior

A named PZERO row on the OpenAI Chat docs (https://docs.spring.io/spring-ai/reference/api/chat/openai-chat.html), same shape as the DeepSeek / vLLM custom base-url samples. No first-party PzeroChatModel required.

Chat-only properties so embeddings stay off this host:

spring.ai.openai.chat.base-url=https://api.pzero.studio/v1
spring.ai.openai.chat.api-key=${PZERO_API_KEY}
spring.ai.openai.chat.model=deepseek-v4-flash

spring.ai.openai.chat.base-url is the /v1 root. Do not paste /v1/chat/completions. Do not set spring.ai.openai.embedding.base-url to this host. Override the default gpt-5-mini model id.

Get a key: https://pzero.studio/agents (sign-in free; min top-up 1 USDC on Base; no starter credits). Live text ids: GET https://api.pzero.studio/v1/models (public, no key).

Smoke:

curl -sS -X POST "https://api.pzero.studio/v1/chat/completions" \
  -H "Authorization: Bearer $PZERO_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{"model":"deepseek-v4-flash","messages":[{"role":"user","content":"Hello from PZERO"}],"stream":false}'

Users who find this issue can convert today even if the docs PR is not merged.

Current Behavior

Spring AI already talks to OpenAI-compatible hosts via spring.ai.openai.chat.base-url. Search for pzero returned none. People looking for prepaid, privacy-first inference still have to guess the host, key format, and that catalog ids are not gpt-5-mini.

I am not asking for a bundled PZERO starter. The existing OpenAI chat auto-config is the seam.

Context

Every AI Credit is at least 20% off $1 list. Usage is paid. Do not start implementation on my behalf until the board says Ready; the snippet is for users today. Keep embeddings, image, audio, and moderation off this host.

Start at the OpenAI Chat documentation page and compare the existing DeepSeek and vLLM custom base-url samples. Add a named PZERO example using the supplied chat-only properties and verify that the /v1 root, model override, API-key placeholder, and embedding exclusion are represented accurately.