docs(api): use public API endpoint prefix

[vrmiguel]

summary

• point the hosted openapi reference at https://api.tembo.io/public-api/
• update explicit hosted api examples and the snowflake integration base url
• fix the remaining hosted url in the self-hosted openapi example

validation

• mintlify validate
• git diff --check
• audited public api routes against monorepo/apps/api/src/server/routes/public-api
• merged origin/main before committing (already up to date, no conflicts)

Want tembo to make any changes? Add a comment with @tembo and i'll get back to work!

      

---

Note

Low Risk
Documentation-only URL corrections with no runtime or API behavior changes.

Overview
Documentation now points integrators and API consumers at the /public-api path on the hosted Tembo API instead of the bare api.tembo.io host root.

API overview (api/index.mdx) updates the sample curl to https://api.tembo.io/public-api/session/list. OpenAPI (openapi.documented.yml) changes the server URL to https://api.tembo.io/public-api/ and refreshes cURL samples for session messages, agent create, and agent trigger. Snowflake (integrations/snowflake.mdx) sets the documented base URL and Python UDF BASE to https://api.tembo.io/public-api, and clarifies self-hosted substitution (e.g. https://tembo.example.com/api/public-api). Self-hosted OpenAPI (openapi.self-hosted.yml) fixes one remaining hosted URL in a cURL example to https://tembo.example.com/api/public-api/....

^{Reviewed by Cursor Bugbot for commit 6455de2. Bugbot is set up for automated code reviews on this repo. Configure here.}

[mintlify]

Preview deployment for your docs. Learn more about Mintlify Previews.

Project	Status	Preview	Updated (UTC)
tembo	🟢 Ready	View Preview	Aug 7, 2026, 12:09 AM

💡 Tip: Enable Workflows to automatically generate PRs for you.

[tembo]

Requesting review from @DarrenBaldwin07 who has experience with the following files modified in this PR:

• openapi.documented.yml
• openapi.self-hosted.yml