Configure a custom external proxy with domain-based routing rules on a Browserbase session

Documented steps

1. Authenticate with the header X-BB-API-Key on POST https://api.browserbase.com/v1/sessions. Reference: https://docs.browserbase.com/platform/identity/proxies
2. Pass proxies as an array of rule objects rather than a boolean; every object needs a type field.
3. For a custom proxy set type to external and provide the server field (your proxy endpoint URL including port), plus the username and password fields, whose values must be injected at runtime from your secret store.
4. Add domainPattern (a regular expression string, for example one matching a single vendor domain) to scope a rule to matching domains only.
5. Order matters: rules are applied in list order and the first matching rule wins for each request. Put specific domainPattern rules before any catch-all.
6. To send some traffic direct with no proxy at all, add an entry with type set to none and its own domainPattern, placed before the catch-all.
7. End the array with a catch-all entry whose type is browserbase and which has no domainPattern, so unmatched requests still have a defined route.
8. Escape dots in domainPattern, since the field is a regular expression and an unescaped dot matches any character.
9. Handle session-creation failure: Browserbase validates proxy connections at session creation time and throws an error if it cannot connect to the specified proxy.
10. Confirm the account is on the Developer plan or higher, which gates both built-in and custom proxies.