Also not an engineer but building my own home.
I would suggest one of four solutions, in no special order, but please check with a structural engineer if you have any doubts.
I would draw attention to the issue that the entire joist system is at risk. Just like parallel joists can reinforce each other, if all are weak, that shared strength may not be dependable. So I'd take it seriously as you are doing.
1) Sister using steel C channel:
Sistering the joist with some C shaped steel channel with an appropriate round (not rectangular! see below) hole cut through it. You'll have to break and re-make the plastic pipe to do this, but that's relativrly easy - PVC cement.
The idea is that C channel will lie with its back (the web) flat to the joist, so it can be very well secured to it, and torque (twisting) won't be a point of weakness.
The C channel wouldn't have to be very thick. It needs a stiffness more than or equal to the joist's original strength for safety and wood is very limited stiffness compared even to thin structural steel.
In steel constriction, be it "I" beams (RSJ), C shaped channel, or rectangular tube (RHS), the strength is provided by the flanges (the top and bottom parralel surfaces) not so much by the web (the connecting part between them).
The idea is that as the beam takes on its load, it flexes, and the flexing means that the 2 parallel surfaces have to stretch at different rates. The thicker the top and bottom flanges, and further apart they are, the stiffer the beam.
Steel takes a lot of force to stretch, so it resists the load well. But this also means that provided the hole is of a size that the channel keeps its shape (which this looks like it will do) the web is very much secondary - which is why I suspect a hole even of this size won't matter to it,provided the steel is firmly fixed to the joist along its length and top and bottom.
In fact, the web's main job isn't to resist load. It's to keep the 2 parallel surfaces aligned and separated in their original position so they would have to stretch under load (thus resist it), and can't just move closer or twist instead.
Note as Jasen says in comments that its important to cut rounded not crude/rectangular holes, to minimise stress and weakness in the steel, which naturally arise much more at cut and sharp corners.
2) Reinforce above/below using steel angle:
You could also place steel angle along the length of the joist above and below the pipe. If that's attached really firmly to the joist so it can't pull through the wood, in theory that would work.
I honestly would have real reservations about this, because whatever you use to secure the angle to the joist, wouldn't have to pull much through the wood at all, over time, to allow the joist to sag. It doesn't have the needed overall stiffness, because the top and bottom aren't held in a fixed position against each other, unlike C channel that innately resists flexing even with a hole in the web.
This would be the simplest, but also my absolute least favourite of the 4 because of that concern.
3) Remaking the joist system to avoid the issue:
You've exposed the joists and clearly are somewhat comfortable with heavy DIY. Alljoists will need fixing anyway. So this might be one other solution, depending on the masonry and other structure of the property.
The joists in that room run "left to right" in the picture. If the property allows and has suitable load bearing walls, one could prop them all either side of the pipe/s (use timber under them so they stay aligned), cut them either side of the pipe, and put doubled or very heavy duty joists running "front to back" parallel to the pipe. Then attach the cut ends of the old joists to your new ones using ordinary joist hangers. Essentially youd be stopping all of the the joists at one side of the pipe and starting them again 200 mm/8 inches further,on the other side of the pipe.
This would work very well, provided there is structurally sufficient bearing for the extra joists at the front and back. While that would not be in the design of the property, the load would spread down through those walls at 45 or 60 degrees, along the ground, so support may not be a huge issue. You might need to ensure good bearing at the top.course of brickwork (engineering bricks below the new joists?) and you'd definitely need to check with an engineer for this. But if they agree, its definitely cheaper to do than steel and any builder could.do it.
4) Move the darn pipe:
Vertically in a box conduit in a corner, outside, wherever. Just reroute the pipes and then replace or sister the damaged joists.
Cheapest and probably simplest of all the 3 I'm sure would work.