docs: add Google Vertex AI and Gemini gateway guide

[rajshah4]

Adds a Google LLM gateway guide covering Google Cloud Vertex AI and Google AI Studio (Gemini API), with Replicated first and Helm second. Matches the AWS Bedrock and Azure gateway guides in #874 and #872: provider selection, credential storage, gateway routes, model profiles, conversation verification and troubleshooting. Adds navigation, integration and installation links, and LLM index content.

Validation: Vertex Gemini 2.5 Flash passed a gateway request and a completed sandbox conversation on GKE with chart 0.74.0 / OpenHands 1.67.0. Replicated release 0.74.0 also passed managed Vertex inference, terminal file operations and a read-only repository conversation. Gemini API configuration is documented and source-checked, but has not yet passed an end-to-end test in this evaluation.

Checks: Mintlify broken links, navigation JSON, shell syntax, YAML parsing and git diff --check passed.

Source verification: Replicated Google configuration, Vertex gateway generation, and Gemini gateway generation.

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[enyst]

I'm an AI agent based on Opus 5.5, helping Engel Nyst (@enyst) with project work.

• Rebase: main removed llms.txt and llms-full.txt in #815 (Mintlify generates them now), so dropping those two files from this PR clears the conflict. #874 adds a card at the same spot in integrations/overview.mdx.
• Checked: the Replicated field titles and per-line routes (config.yaml#L389-L436, openhands.yaml#L1046-L1054). Also the volumes/volumeMounts/envVars pattern, which matches what Replicated renders, and the openhands/<alias> profile with the :4000 base URL, which matches LITE_LLM_API_URL (_env.yaml#L354-L359).
• One accuracy point inline: where the Replicated credential ends up. It also affects the opening sentence (lines 9–10).
• #875 refers to this guide, so merging this one first lets #875 link to it.

[enyst]

On Replicated, this file doesn't stay in the LiteLLM pod. The installer also copies the service-account JSON into global.agentServerEnv as VERTEXAI_CREDENTIALS, so every sandbox gets it (openhands.yaml#L1017-L1020). Could you say that here, and soften "The Google credential belongs to the bundled LiteLLM gateway" on lines 9–10? The Helm path is described correctly. Admins will want to scope that service account accordingly.

[rajshah4]

Thank you for pointing this out. Updated both the introduction and Replicated section to explain that Vertex credentials also reach sandbox environments. We confirmed this with a boolean-only terminal check on our evaluation instance, without displaying credential values.