I would spend 255/50 R20 to the 275/45 R20 or 285/45 R20 .
What would you think of the increased consumption knowing that I am an average 9.5 l / 100 km ?

https://tiresize.com/comparison/

Negligible - the circumference is about 1% less with the 275's

You should keep all 4 the same as that could still put too much stress on your differentials if you mix them

Don't forget to inform your insurance company that you made a modification to the manufacturers specification

The 285's have an almost identical circumference

For the tires, I obtain the homologate size from the boss of my technical control center.
As you say, It will be certainly better to advise the insurance company to be quiet

Hear is the sheet fot the 4.4 TDV8’s tire

Click image to enlarge

I went up in tyre width (but not a significant change in diameter) when I put off road tyres on my L405. Fuel consumption was noticeably worse (5-10%). Rolling resistance, I'd guess.