Implement APR repo-transfer-to-customer initiation via GitHub's transfer API

[JSONbored]

Context

#7590 decided APR customers get an optional, explicit transfer-to-their-own-account flow using GitHub's standard repository transfer mechanism, rather than owning the repo from day one. No code exists yet for this.

Requirements

Add a function that initiates a GitHub repository transfer from the loopover-controlled org to a target GitHub account, using the GitHub REST API's "Transfer a repository" endpoint (POST /repos/{owner}/{repo}/transfer) with the target account's login as new_owner. GitHub's transfer flow requires the recipient to accept via a confirmation email within a time window and does not complete synchronously — this function's job is to initiate the transfer and return whatever status GitHub's API response provides; it must not assume or report the transfer as complete just because the API call succeeded.

⚠️ This issue does not cover: detecting when a pending transfer is accepted/expires (separate follow-on concern, not scoped here), any UI for the customer to request a transfer, or anything about when a transfer should be offered (a product/UX question, not this issue's job). Deliverable is exactly: given a repo and a target account login, call the transfer endpoint and return its response, tested.

Deliverables

• A function that calls the transfer endpoint given a repo full name and a target account login, using the App's installation token (same token source as the repo-creation issue).
• Unit tests covering: a successful transfer-initiation response, and at least one realistic error case (e.g. the target account doesn't exist, or the caller lacks admin access to the repo) handled without an unhandled exception.
• A short doc comment on the function stating explicitly that a successful API response means "transfer initiated," not "transfer complete" — this distinction matters for anything that later builds on top of this function.

Test Coverage Requirements

Standard 99%+ Codecov patch target for src/**; mock the GitHub API in tests, no live transfer calls.

Expected Outcome

A tested, reusable way to initiate a repo transfer to a customer's account, correctly modeling that GitHub transfers are asynchronous and acceptance-gated rather than instantaneous.

Links & Resources

• The APR repo-creation issue (sibling — same token-acquisition pattern)
• Design spec: APR repo creation under the submitting customer's own GitHub account (twice-corrected) #7590 (the decision this implements)
• GitHub REST API: "Transfer a repository" (POST /repos/{owner}/{repo}/transfer)

[linear-code]

JSO-5399

[JSONbored]

Parked (2026-07-21), not deleted: repos currently stay under the JSONbored personal account for both creation and operation (see the corrected #7590/#7637) — there's no separate owner to transfer to yet, since the platform operator and the repo owner are the same account right now. This issue becomes relevant once there's an actual separate paying customer who should end up owning their own repo. Leaving open but not active work — don't pick this up until a real customer-facing APR flow exists to attach it to.