Problematic (it is not so easy) curtain rod

In the hardware store, there are 2.40 m rods in one piece. There are also extendable 2.10 - 4 m rods.

The specialty store is also happy to welcome customers.

If you have to "juggle" with the rods anyway (because of electrical work), I would first install the rods and then have the curtains made to measure.

Do you have wallpaper or directly painted plaster? What do you think about simply gluing the middle support? I haven't tried this myself with curtain rods, but good mounting adhesive can really withstand extreme tensile forces; in your case, it would even be just 90-degree shear forces and more for stabilization than for actual support. We have a lamp hanging like that (capitulation after trying dowels in old sauerkraut particle board, don't ask), the adhesive specifies 30kg tensile strength per cm², and there are even better ones.

Attach the curtain rod to the wall on the right and left and support the construction with 1-2 ceiling mounts using an almost invisible nylon thread. Then you have combined stability and appearance.

Someone have an idea for our installation situation with a 2.4m curtain rod - stable without a 3rd bracket?

hm... we had curtain rods in the old house, those metal things from Ikea. I don't think they were extendable back then. But they were stable without a center bracket, even at 2.50 length. I can't recommend a tension wire, that would sag. What kind of curtains are those? Are they supposed to be closed? Are they heavy or rather fluffy?