synapse_pushers metric overcounts on every /pushers/set request

[squahtx]

When handling a /pushers/set request, Synapse removes any matching pushers belonging to a different user, then calls PusherPool.add_pusher:

synapse/synapse/rest/client/pusher.py

Lines 106 to 125 in fe1daad

	if not append:
	await self.pusher_pool.remove_pushers_by_app_id_and_pushkey_not_user(
	app_id=content["app_id"],
	pushkey=content["pushkey"],
	not_user_id=user.to_string(),
	)
	try:
	await self.pusher_pool.add_pusher(
	user_id=user.to_string(),
	access_token=requester.access_token_id,
	kind=content["kind"],
	app_id=content["app_id"],
	app_display_name=content["app_display_name"],
	device_display_name=content["device_display_name"],
	pushkey=content["pushkey"],
	lang=content["lang"],
	data=content["data"],
	profile_tag=content.get("profile_tag", ""),
	)

PusherPool.add_pusher eventually creates a new pusher to replace the existing one:

synapse/synapse/push/pusherpool.py

Lines 354 to 359 in e24ff8e

	byuser = self.pushers.setdefault(pusher_config.user_name, {})
	if appid_pushkey in byuser:
	byuser[appid_pushkey].on_stop()
	byuser[appid_pushkey] = p
	synapse_pushers.labels(type(p).__name__, p.app_id).inc()

Critically, it increments the synapse_pushers metric, regardless of whether it replaced an existing pusher, so stopped pushers can be included in the count.

[squahtx]

The bug was introduced in #7855