What the field controls
By default, web pages cannot connect directly to an extension's runtime messaging. externally_connectable opens that channel for listed origins and extension IDs. The extension must still implement message handlers.
The field is about communication, not DOM access. A site does not need a content script to send a message if the origin is allowed, although the extension decides whether to respond.
Related pages:manifest viewerweb_accessible_resources security
Why broad origins matter
An entry of <all_urls> means any website can attempt to connect. If a handler exposes privileged operations without validating the sender, another site could trigger them. The risk depends on the handler's authorization logic.
Even a narrow origin list deserves review when it includes sites the publisher does not control, because a compromised site could send crafted messages.
Related pages:extension CSPsource analyzer
What to look for in the code
Search for runtime.onMessageExternal and runtime.onConnectExternal handlers. Check whether the sender origin is validated, whether messages are authenticated and whether the handler can access sensitive APIs or data.
A static analyzer can flag the manifest value and the handler references, but it cannot prove that exploitation is possible. Treat findings as review prompts.