I play in a metal/rock band and “had” to switch from bass to guitar, which means that I have to change my whole gear. I plan on getting a two channel amp and to use a multi-effect that is able to switch the canal of the amp (currently looking for a boss gt-10)

I am pretty much limited to used gear and have found someone in my area selling a nice H&K Warp X. The problem is that, while this amp has only two channels, its footswitch (H&K FS-2) also handles the fx-loop switching. I’m afraid that the boss gt-10 won’t be able to switch channels on that amp.

Has anyone experience with that setup or knows if how the Warp-X handles a "basic" footswitch?

Unfortunately the only way you'll be able to use your GT-10 as the foot switch would be if the amp had midi capabilities which it appears to not have. Fortunately, it just requires a basic 2 button foot switch so you should be fine with just using a generic switch like a Boss FS6.
Satan. Grant this man the gift of revenge against his foes at the Food Network.
The amp is actually sold with its original footswitch. But I wouldn't be able to switch the amp and the effects at the same time with the push of only 1 button, which is what I'm trying to achieve

PS: that amp has a midi extension possibility, but that costs half the price of the amp