>If that is the case then why even develop Ariane6 as an expressed rival to the Falcon9 of 2017 instead of just subsidising Ariane5 indefinitely?

Because it makes more money, or rather means Ariane needs less subsidies.

More or less, but primarily, Arianespace is there to provide independent European capability to space. That it dominated the launch market for a bit was a happy additional benefit, but not the primary mission.

>IS pushing the shell

By a negliglible amount. There are actual range-boosted shells with rocket motors which gain significant thrust from the shells actually accelerated in flight.

Base-bleed is not that and for simplicities sake these shells aren't said to be propelled by it, they just have less drag.

>and a "negative pressure" behind the projectile.

And quite a lot. For an artillery shell this can be as high as 40% of the drag. Modern artillery shells have pyrotechnic charges at the back to reduce this. They aren't pushing the shell, they just fill up the empty void with gases, reducing the drag by a lot. That type of ammunition called base-bleed can have up to 30% longer range.

E.g. a German PzH2000 self-propelled howitzer firing a base-bleed shell in Ukraine:

https://pbs.twimg.com/media/FoVlKRDWAAACjsY?format=jpg&name=large

Desert just means dry. All of it is frozen though.