Document PULUMI_TFE_DOMAIN for self-hosted operators

[nyobe]

Summary

• Add PULUMI_TFE_DOMAIN to the self-hosted API component env vars table (components/api.md)
• Add optional tfe.{domain} DNS record to the networking operations guide (operations/networking.md)

Companion to https://github.com/pulumi/pulumi-service/pull/42418 which moves the TFE-compatible state API to a dedicated subdomain. Self-hosted operators need to know about the new env var to enable the feature and the DNS record to route traffic.

Test plan

• Verify rendered markdown looks correct in the Hugo preview

🤖 Generated with Claude Code

[claude]

Docs review

Tight, well-scoped change. The new env var row matches the existing table style and the DNS bullet cleanly extends the list. A few minor notes:

Minor: capitalization inconsistency between the two files

components/api.md line 78 uses (Optional) (capitalized) while operations/networking.md line 75 uses (optional) (lowercase). Not wrong either way, but worth aligning. Suggest lowercase in both, since the env-var-table convention elsewhere on the page tends to use sentence-style descriptions and (optional) reads as a parenthetical aside rather than a label:

In content/docs/administration/self-hosting/components/api.md line 78:

suggestion | PULUMI_TFE_DOMAIN | (optional) The domain for the TFE-compatible state backend API, e.g. \tfe.acmecorp.com`. When set, the service exposes a Terraform/OpenTofu-compatible state API on this domain at `/api/v2`. When unset, the TFE-compatible API is disabled. Requires a DNS record pointing this domain at the same load balancer as the API. |
`

Nit: terminology echo on the networking bullet

networking.md line 75 says "required only if `PULUMI_TFE_DOMAIN` is set" — the "required only if" phrasing reads slightly awkward next to the leading "(optional)". Consider:

In `content/docs/administration/self-hosting/operations/networking.md` line 75:

`suggestion

• `tfe.{domain}` - (optional) for the TFE-compatible state backend API; required when `PULUMI_TFE_DOMAIN` is set
  `

Pre-existing (out of scope, FYI only)

The link anchor `#environment-variables-for-core-infrastructure` resolves correctly, but the H2 `## Environment Variables for Core Infrastructure` (api.md line 65) is Title Case while AGENTS.md specifies sentence case for H2+. Not introduced by this PR — flagging only because you're linking to the section.

Verified

• ✅ Anchor target `#environment-variables-for-core-infrastructure` exists in api.md
• ✅ Internal link uses absolute canonical path per AGENTS.md
• ✅ New env-var row formatting consistent with surrounding rows
• ✅ Terminology ("TFE-compatible state backend API") consistent across both files
• ✅ No file moves, so no aliases needed

LGTM with the optional polish above. Mention @claude if you'd like another pass after changes.

[pulumi-bot]

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