Set x-synthetic-id header on integration routes

[prk-Jr]

Integration proxy responses were missing the x-synthetic-id header because handle_proxy dispatched to integrations without adding it. This caused identity tracking to break for first-party re-hosted integrations like Permutive's secure-signal endpoint.

Centralizing the header logic in handle_proxy ensures all current and future integrations automatically include the synthetic ID, rather than requiring each integration to implement it manually.

Fixes #205

[aram356]

Good start but should use funcitons in cookies.rs

Please don't make the feature branch have this long name. Please stick to feature/short-name

[aram356]

🔧 We need a more thorough fix:

publisher.rs:201-211 uses manual string splitting to check for an existing synthetic cookie:

let has_synthetic_cookie = req
    .get_header(header::COOKIE)
    .and_then(|h| h.to_str().ok())
    .map(|cookies| {
        cookies.split(';').any(|cookie| {
            cookie.trim_start().starts_with(&format!("{}=", COOKIE_SYNTHETIC_ID))
        })
    })
    .unwrap_or(false);

While registry.rs:622-626 uses handle_request_cookies with CookieJar:

let has_synthetic_cookie = handle_request_cookies(&req)
    .ok()
    .flatten()
    .and_then(|jar| jar.get(COOKIE_SYNTHETIC_ID).map(|_| true))
    .unwrap_or(false);

These should use the same approach. The CookieJar version is more robust (proper cookie parsing).

Since we already have cookie utilities in cookies.rs, suggest adding a set_synthetic_cookie(settings: &Settings, response: &mut Response, synthetic_id: &str) helper there that handles the append_header call. That way both publisher.rs and registry.rs call the same function, and the append_header fix and cookie creation logic live in one place.

We don't need has_synthetic_cookie check we was primarily for logging we should always set COOKIE_SYNTHETIC_ID

[aram356]

🔧 Duplicate test

These three cookie_jar_* tests are testing parse_cookies_to_jar from cookies.rs — they should live there, not in the registry module. cookies.rs already has equivalent coverage (test_parse_cookies_to_jar, test_parse_cookies_to_jar_emtpy, etc.), so these are duplicates and can be removed.