Right of way - Old drainage of unknown origin

Three plots further, an old drainage pipe was uncovered during the excavation for the basement [...], which now causes water to repeatedly enter their basement. [...] The affected property owners understandably insist on a quick solution,

... however, they should rather insist on a clarification, which they themselves should initiate. Before they try to share their hardship with you, they should first stop it. Someone is obviously diverting their water to them. If I were in their place, my first step would be to find out who has had such a right registered. And if there is none: file a complaint against unknown persons to identify the offender; inform the competent authority (which would usually be located at the district administration). No one is allowed to impose their surface water burden on another. For legal advice, seek an environmental lawyer; with a "general practitioner" lawyer, you would probably go under. However, for a letter pointing out their homework that cannot so easily be assigned to you, such a lawyer might suffice preliminarily.

Yes, lawyer. It is quite possible that some environmental agency will cause trouble. It is similar to having dinosaur bones found at your place or the Amber Room. In a way, you are powerless...

Without details about the type of drainage and the local conditions: My parents had something similar - the building area was previously agricultural land (field). When excavating the foundation pit, two drainage pipes were also found - these were clay pipes, about 15 cm in diameter, which the farmer had laid decades ago. They briefly checked in which direction the course went to the property boundary, dug there, inserted the pipe, and filled it again.

I wouldn't be interested either in where they come from or where they lead - dig up, close it up.

(...)
I wouldn’t be interested either in where they come from or where they are going – dig up, seal off

The crucial detail here is that the municipality was informed.
So "cut off, seal it, no one finds out" is off the table.

We were advised the same by the general contractor back then. If you find a shard of clay... pocket it, throw it away, eat it, whatever. Just don’t tell anyone about it.

By now, it’s far too late for that, the municipality talks about easement rights. Cutting off the thing now would be like spreading your own DNA on a found corpse again...
Lawyer. Nothing else. This is no joke... because, dear friends. If this comes from a farmer. Who among you knows what was insured to him in the year 19xx? Possibly even in writing? As far as I know, that would still be valid even if the emperor approved it back in 1917...
You can get yourself into such unbelievable trouble...

I would also be extremely cautious with the right of way. In the end, no one knows what restoration of the garden/terrace looks like anymore. Plus, 100m2 are poorly usable. Just calculate with your m2 price what kind of sum that is. I’m not that technically savvy, but why don’t those affected let it infiltrate on their own property? Why does the new pipe have to go through your property? A sketch would surely help those more experienced as well.

but why don't those affected let it seep away on their own property?

The water of the unknown third party does seep away, but unfortunately into the building fabric of their basement

Why does the new pipe have to go through your property?

Because water flows downhill, and the improper question "could you please take our problem?" asked to higher-lying neighbors would be pointless, whereas asked to the OP it is just cheeky :-(