Is your feature request related to a problem? Please describe.
Currently when the linkcheck builder encounters a timeout while checking a link, the corresponding link will be reported as broken.

This makes it difficult to distinguish between webservers that are slow to respond, as compared to received responses that indicate that a given hyperlink no longer returns useful information. That distinction could be valuable, for example to help determine whether hyperlink unavailability is due to transient or network-related conditions.

Describe the solution you'd like
An additional reporting status for the linkcheck builder. The simplest name for this status would be timeout.

Describe alternatives you've considered
TODO: are there alternatives approaches that would be an improvement on this?

Additional context
Technically the linkcheck builder has (at least) two kinds of timeouts - there's a low-level network socket timeout, which we set to 5 seconds, and there's the per-hyperlink request timeout, relating to the time that the (connected) client will wait for a response from the webserver.

• Opened following discussion in linkcheck build never ends #11853.