Flight Instructor reported while instructing student practicing landings; ATC instructed another aircraft to make a left turn into the student and Instructor causing the Instructor to take evasive action to avoid a midair collision.

Narrative

Conditions were clear skies; light winds out of the north. Landing and departing runway 31R at RHV. I was with a student who was practicing landings. RHV airport located on east side San Jose has 2 runways; but extensive airport construction has been happening for some months now. Recently; they decided to allow pattern work with only one runway open. Unfortunately; I think this has a severe impact on safety; especially on weekends with a higher volume of aircraft coming in and out.My student and I were on an extended left downwind for runway 31R. We were over 10 miles out from the airport; and I was beginning to assume that due to the busy nature of arrivals and departures; RHV Tower forgot we were closed traffic. I advised that we were looking for a base turn. They told us we could turn now; and we were #3. I had ADSB-in on board and could see traffic around us. During this downwind extension; I heard another pilot in Aircraft Y was told to go around and make left traffic; as there was an aircraft still on the runway when he was short final. At RHV they almost always extend our downwind for spacing. But to this pilot who had just went around; he was already 5 -7 miles south of the field when RHV Tower said; 'maintain 1500; overfly 31R and make left traffic'. This uncommon instruction confused the pilot due to how far they already were from the field. That instruction would've made sense had he been midfield downwind for right pattern; but he wasn't. He was confused. I was with my student at 1500 feet; on the glideslope; approaching to land. I had traffic on short final ahead of us; and traffic behind us. The pilot who got the uncommon instruction asked the tower 'Do you just want me to turn base now?' RHV Tower said 'yes; turn base now'. I watched in horror as this airplane turned left base directly into my student and I; at the exact same altitude. I tried to make a call on frequency to say; 'please don't turn we are right here!' but I do not think it transmitted. I took controls and had to evasively dive the airplane down to avoid him. The radio was so filled with chatter it was impossible to get a word in before he turned. In a panic I told the tower 'You just turned that airplane into us on final!' They claimed; 'He is at 1500 overflying the field to make left traffic'. I said that I understood that; but we are at 1500; so he turned left into us at the same altitude. RHV tower responded with 'Roger'. ATC made no attempt to confirm that the airplane turning left base had either me; or the other 2 people on final in sight. I spoke with the other pilot afterwards and they confirmed they had no idea people were on final until he heard me. I ended up calling RHV tower once on the ground; to see if I could've done anything differently to have that unfold better. I tried to explain that on a 7-8 mile final from RHV; we have to maintain a higher altitude like 1500 to be on the glideslope. They said I didn't do anything wrong; the other pilot had us in sight. I know now that this is NOT true. I was not left feeling good with that interaction from ATC. I know in my heart that if I was not on board this airplane; my new students lack of situational awareness could've led to a real MAC (Mid-Air Collision). To have that occur in clear conditions at a towered airport is unacceptable.RHV Tower is not equipped to handle the high volume of traffic on weekends and offer pattern work. A few months ago; when they had only 31L open but did not allow pattern work; events like this never occurred. I believe task saturation was causing RHV tower to confuse themselves with their instructions during this. I estimate there was 3 people in the pattern; 5 - 6 people inbound; and 3 -4 planes holding short waiting to depart. During this unfolding; I heard them call multiple aircraft by the wrong tail numbers. For safety's sake I will not be doing any pattern work at RHV until both runways are open. The pilot who turned into me had a lack of situational awareness as well. Had he been listening to the frequency more; he would've known there was multiple aircraft on final.