gauge.set_function() doesn't work in multiprocess mode

Multiprocess mode's collect() reads the registry files and aggregates metrics that have been written to prometheus_multiproc_dir.

This doesn't work with gauge.set_function() which does not record its value. The provided function is just called during collection.

That means with the following code:

registry = CollectorRegistry()
Gauge("test", "test", registry=self._registry).set_function(lambda: 100)
multiprocess.MultiProcessCollector(registry)

The output will be:

# HELP test test
# TYPE test gauge
test 100.0
# HELP test Multiprocess metric
# TYPE test gauge
test{pid="10705"} 0.0

Current side effects:

• If any mode other than all or liveall is used, the pid tag won't be included. This results in duplicate metrics being reported to Prometheus. Prometheus currently only uses the first metric it reads, which is non-deterministic due to iteration over the registry's dictionary.
• If registry=None to avoid double reporting, only the default value of 0.0 is reported.
• Current way to work around it is to use the mode all and to ignore gauges in Prometheus and with the tag pid.

Proposal:
I'm not sure how you could incorporate set_function into the multiprocess registry and I'm not convinced how useful of a feature it would be. Is it reasonable to add a new multiprocess_mode: exclude which would prevent the incorrect 0.0 value being reported? Or would it be better to just add documentation to recommend using two independent registries?

Reproduce the discrepancy using multiprocess.py's collect() entry point and the registry.py set_function() behavior, with prometheus_multiproc_dir configured. Compare the reported values across multiprocess modes and determine the expected handling for set_function(); done means the chosen behavior is documented and the duplicate or incorrect 0.0 reporting is addressed.