Add deployments executorRootPath and PULUMI_ENV docs

[rgharris]

Closes https://github.com/pulumi/pulumi-service/issues/38301

Documents executorContext.executorRootPath in deployments docs and REST API.

Includes follow-up context from https://github.com/pulumi/pulumi-service/pull/38896 by documenting that PULUMI_ENV uses PULUMI_ENV_FILE when executorRootPath is configured.

Unreleased product version (optional)

Waiting on https://github.com/pulumi/pulumi-service/pull/38896 to ship

[claude]

Docs Review

Overall, this is a clear, well-structured addition that covers a useful feature. A couple of style issues to fix.

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content/docs/deployments/deployments/using/settings.md

H2 heading — sentence case required (line ~134)

Per the style guide, H2+ headings must use sentence case, not title case.

## Custom executor root path {#custom-executor-root-path}

Missing comma after introductory phrase (line ~198)

By default, this file is `/PULUMI_ENV`. If you configure a [custom executor root path](#custom-executor-root-path), Deployments sets `PULUMI_ENV_FILE` to `<executorRootPath>/PULUMI_ENV` and uses that file instead.

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content/docs/reference/cloud-rest-api/deployments/_index.md

No issues found. The new JSON example and property table row are accurate and consistent with the surrounding content.

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Summary

Two minor style fixes needed in settings.md. The technical content is accurate, the cross-references are appropriate, and the bash example update using ${PULUMI_ENV_FILE:-/PULUMI_ENV} is a nice improvement for portability.

Mention @claude if you'd like another pass after making changes.

[pulumi-bot]

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[CamSoper]

Fixed two minor style issues:

• Heading case: "Custom Executor Root Path" → "Custom executor root path" (sentence case per style guide)
• Added missing comma: "By default, this file is..."

Otherwise this is clean — good addition of the executor root path docs and the PULUMI_ENV_FILE context.

[pulumi-bot]

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