Switch the caller's existing subscription to a different paid plan.

Requires manage scope. Refuses if the account has no active subscription (no_subscription, 409 — use /v1/billing/checkout to start one instead). plan_id must name a real, paid, currently-purchasable plan different from the account's current one (bad_request, 400, for an unknown, free, unpurchasable, or already-active plan_id). Upgrades swap the subscription's price immediately with no proration charge, billed in full next cycle (effective: "immediately"). Downgrades are scheduled for the next renewal so the caller keeps what they already paid for until the period ends (effective: "at_period_end").