Single engine Flight Instructor reported taking evasive action to avoid pattern traffic that ATC failed to separate resulted in a NMAC.

Narrative

The pattern at SQL was super busy; but I do not want to give Tower an excuse. There were supposedly 8 planes in the pattern when the event occurred. My student was climbing out of SQL to join the traffic pattern. In our crosswind to downwind turn all of the sudden I look at our Multi-function Flight Display (MFD) and notice an aircraft same altitude less than a mile away. They're holding our altitude at 800 ft right for the pattern. I was not told any traffic was following; or any traffic alert warning from our Tower at this time. I immediately began to climb as we were on converging paths. I climb to about 1;100 and see the helicopter that we were not made aware of at all flying right underneath our aircraft at about 900 feet so only 200 feet below us. I later called Tower on their land line to see what happened. They said supposedly the helicopter was non english speaking and had stopped responding to them. If that was happening; I would've at least liked a traffic avoidance call. They were so worried about extending everyones downwind with so many people in the pattern they didn't notice the two aircraft same flight level flying right at one another. 'Having a busy pattern' is no excuse. The Tower is supposed to provide separation services for us in their delta and had I not taken the controls from my student and climbed as an evasive action I don't think today would've had the same result. This is concerning that our Tower was unable to provide safe guidance or separation from two aircrafTS taking off and one remaining in the pattern; that had been in the pattern for the previous 30 min. Also; helicopters typically make left traffic at our airport; so not being made aware of a non standard helicopter making right traffic would've been helpful.