Add BADCODE release/update env vars or aliases

[badcuban]

Priority: P1

Why

Release and updater configuration still uses T3CODE_DESKTOP_* names even when pointing at badcuban/badcode. We should either rename these to BADCODE_* or add aliases with clear precedence.

Evidence

• docs/release.md:37 instructs $env:T3CODE_DESKTOP_UPDATE_REPOSITORY = "badcuban/badcode".
• .github/workflows/release.yml:146 sets T3CODE_DESKTOP_UPDATE_REPOSITORY.
• scripts/build-desktop-artifact.ts reads T3CODE_DESKTOP_UPDATE_REPOSITORY and documents T3CODE_DESKTOP_* flags.

Acceptance criteria

• Define BADCODE_DESKTOP_* names for release/update configuration.
• Add aliases for existing T3CODE_DESKTOP_* variables where needed.
• Document precedence if both old and new vars are set.
• Update release workflow and release docs.
• Add coverage for old-var and new-var behavior.

[badcuban]

Diagnostics follow-up from May 26, 2026:

The desktop trace repeatedly logs desktop.updates.handleUpdaterError and failed to check for updates every poll interval. The error is a 404 while fetching https://github.com/badcuban/badcode/releases.atom.

This confirms the updater path is already pointing at the BadCode repo, but the release/update behavior is not yet private-repo/release-feed aware. This should be handled as part of the BadCode release/update env/config cleanup here, or coordinated with the Windows-first release-surface issue.

[badcuban]

Near-term updater decision from May 26, 2026:

The repository can stay private for now. The immediate requirement is that updates work for the owner (badcuban) on an authenticated development/test machine, especially for 0.0.1 -> 0.0.2. Later, when BadCode is open sourced or release assets move to public hosting, the updater should work for everyone without private-repo auth.

Implementation note: normal browser/GitHub CLI authentication may not automatically be visible to electron-updater from a Start Menu launch. As part of this issue, decide and document the private-repo auth source for packaged app update checks, such as GH_TOKEN/GITHUB_TOKEN, GitHub CLI token discovery, or a BadCode-owned generic feed. The first private alpha path only needs to be reliable for the owner, but it should fail clearly when runtime auth is missing.

[badcuban]

Fixed in commit f8250e11 and released in v0.0.7: BADCODE_DESKTOP_* env vars are supported with precedence over legacy T3CODE_DESKTOP_* aliases, and the workflow/docs/tests now use the BadCode names. Release: https://github.com/badcuban/badcode/releases/tag/v0.0.7