Electrician here from Australia. Different standards but the concept is the same.

I should preface this with, Electrical work can be dangerous especially if you don't have a residual current device to protect you. A circuit breaker protects the cables and a RCD protects us. Call a professional if you don't feel confident.

Be sure to isolate and turn off your mains or individual circuits. Use a volt stick and a meter and check for dead and also on a known power source and then recheck for dead.

Now to the wiring.

It sounds like you have something called 'loop at the light's'

Basically you have a permanent active, neutral and an earth that is ran around the house to each light fitting. Then you have two cables down to the switch, one connected to the permanent active and the other connected to the switch active of the light fitting. Typically in Australia this is white = switch wire and red = permanent active (but not always)

If your light fitting is in the centre of the house it will have an in and an out for each of the cables as it loops from the last room into the next room.

It looks like the fitting neutral on the left is the blue, the two blacks next to that are the incoming and outgoing neutrals, the two Red's next to that are 'probably' the permanent actives, the next two are probably red permanent and in this case black switch wire (maybe), then you've got the fitting switch active on the far right, which is linked internally in the fitting to the switch active down to the switch.

You'll need to test it (I can't stress this enough), as the picture isn't that clear but that is what makes sense to me that the neutrals and permanent actives (are each seperately) in a linked bar inside the fitting.

You're also relying on the fact that someone has wired it correctly beforehand. I find heaps of wiring that they use the black cable as permanent active or blacktive as we call it, which should never be done.

You've also got solid copper wiring N and L so be careful not to over tighten and crush the copper in the fitting as this is how the copper strands snaps. We usually double over and fit it off for this reason in case of breakages it has a redundancy.

Flex means flexible cable btw. N means Neutral and L means Line which is Permanent active. Switch can be SW or SA.

Goodluck and I hope I have explained it well enough to make some sort of sense.

Edit: I re read your problem. I'd check for single copper breakages in the fitting as I've listed above. Basically pull each cable out one by one and replace it and check each strand is not broken. (With the mains off).

Here's an image which may help you understand what's going on: https://images.app.goo.gl/77AgfRcw51yCUvmq6