A TRACON Controller reported they turned an Air Carrier at 4;000 feet away from an unidentified VFR aircraft also at 4;000 feet averting a possible mid air collision.

Narrative

Aircraft X came to me from ZZZZZ descending to 4000 ft. on the ZZZZZ1 Arrival. I noticed a VFR target with no mode C readout that was going to get real close to Aircraft X's flight path. I issued traffic and turned the Aircraft X a bit thinking the target was likely down low like the other hundreds of aircraft with no mode C and I didn't want to over react. Meanwhile; the ZZZZZ Controller noticed the same target and reached out to ZZZ Tower to see if he was on their frequency. He was and the ZZZZZ Controller asked them to have the aircraft squawk altitude. When he did; I realized the aircraft was actually at 4000 ft. I issued traffic; increased the turn. Targets were already not going to merge from the other heading issued and attempted to descend the Aircraft X below the target so wake turbulence would hopefully not be a factor for the VFR aircraft. I'm pretty sure the Aircraft X pilot had an RA when the mode C popped up on the VFR; but he didn't tell me that and just said 'Thanks a bunch; you really saved the day.' I believe if I had not turned the Aircraft X; there would have been a mid air collision; and that's not an exaggeration.Was it bad the VFR aircraft was flying so close to Bravo airspace maybe inside the mode C veil directly through a 25 mile final to a busy international airport; at an IFR altitude; not talking to ATC; with no mode C? Yes; I think that was pretty dumb. That isn't the issue. The issue is the same one multiple Controllers have filed multiple [reports] on year after year. Our Bravo airspace design is terrible and needs to be extended to encompass our final approach courses. I don't care about VFR pilots complaining; AOPA fighting it; or the politics involved. I have passed on filing many MANY of these [reports] in the past year or two for near misses that were saved at the last minute by Controllers because I thought my point was made and it would be addressed. There seems to be no forward progress on this at all. Is it going to take people dying for something to move forward? There will be a trail of [reports] about this issue to look at and point to it being a known issue when that happens.