Fix AirPlay PIN pairing on tvOS 27

[JaviSoto]

Summary

• Send the configured remote name as X-Apple-Client-Name during AirPlay HAP pairing.
• Use a per-pairing header copy for /pair-pin-start and all /pair-setup requests.
• Add a fake-receiver regression test covering the complete four-request HAP pairing exchange.

Addresses the no-PIN AirPlay HAP pairing path reported in #2866.

This does not address the separate post-PIN HTTP 470 or Companion pairing failures discussed in that issue.

Background

On an AppleTV11,1 running tvOS 27.0 (24J5325d), AirPlay pairing returned HTTP 200 and tvOS generated a four-digit passcode, but the receiver suppressed the PIN UI because the request had no client name:

passcodeString is empty or clientName is nil. Bailing.
{passcodeLength=4, clientNameIsNil=YES}

pyatv already carries the configured display name inside encrypted M5, but that arrives after tvOS needs the name to present the PIN. Adding X-Apple-Client-Name to the initial HAP pairing requests caused the PIN to appear immediately and the normal pairing flow completed successfully.

This is intentionally scoped to HAP/AirPlay 2 pairing. Legacy pairing, transient authentication, verification, and module-global headers are unchanged.

Testing

• Added a receiver-boundary functional regression that checks the configured name on /pair-pin-start and all three /pair-setup requests.
• Ran the complete chickn validation pipeline successfully.

AI-use disclaimer

Codex with GPT 5.6-Sol were used in the creation of this PR, but everything was reviewed by me.