Is it possible to add a new type of invasion (such as the pillagers) but changing the attackers???

yes but no, with the block called spawn at x y z entity etc

but no for the boss bar unless u do code

I think you can replace current raids with custom tag "minecraft:raiders" (for entities) and making it "replace:true" while editing code. But if you want to make it separate one, then RexCerv idea is where you need to go ^^