UKH

as it says on tin

The closures are at night, schedule here:
https://www.tunnelmb.net/en-US/news/april-july-2023-maintenance-works-and-s...

No they aren't... From your link it's from 17h00 on the 4th of September until 22h00 on the 18th of December.

1 fermeture de la durée de 15 semaines consécutives, à partir de lundi 4 septembre 17h00
jusqu'à lundi 18 décembre 2023, 22h00.

And there'll be the same thing in 2024 and no doubt the following years.

There are night-time closures between 17 April and 13 June, but the September to December closures are complete closures. 

My apologies to the OP.

What are they closing it for?

If you read the link in Fredt's first post, you'll see it's for renovation works on the road deck and complete reconstruction of two portions of the tunnel vaults. 

mainly an asbestos problem I think

"amiante" is asbestos

Cette mesure immédiate fait suite à la découverte de traces ponctuelles de fibre d’amiante dans certains éléments constructifs lors des travaux, et doit permettre une nouvelle inspection détaillée pour d’éventuels travaux complémentaires d’assainissement.
 

I can't find the links, but I read last year that the first closures were for testing and to better define the works programme but they do expect it to be closed every autumn for several years. 

https://www.ledauphine.com/transport/2023/03/20/le-tunnel-du-mont-blanc-fer...

The first two closures (presumably 2023 and 2024) are intended to renovate 1200m of the tunnel (so 10%) and to plan for fixing the other 90%. This would imply another 20 years of closures at the same rate...

The Swiss approach (see the Gotthard road tunnel) would be to dig a second parallel tunnel then when that's finished close the existing one to renovate it in one go.