I recently tried the Brenizer method but found that it is tedious compared to just using the panoramic mode on my Fuji XT-10 which automatically stitches the photos together. The problem is that I can only swipe horizontally or vertically when in panoramic mode but not both. Is there any way one can do in-camera multi-row panoramas?
No, you can't.
The panorama mode on your camera is very basic, all it does it roughly stitch the edges. In order to correctly make a Brenizer you need to do a more in depth blending that takes in to account lens distortion and vignetting. That is something that takes a powerful computer a few minutes to do, so your camera certainly wouldn't be able to do it well.