They have a carpenter's type of glue that should work well. People use something like that to glue down countertops if they are hard to screw onto cabinets.

That gets stapled, and then touched up with the TUK. Plus an OCM.

I would apply glue to the edge of the side panel and the edge of the back panel you are installing, let the glue tack up, then use staples or brads or even a pin nailer, through the back panel into the side panel. Be careful to nail straight, so the brad or whatever doesn’t exit through the side panel. If you use a pin nailer, you won’t even need to do any touchup. I’d use as few brads or staples as possible; the glue should do the holding, the fasteners just keep things in contact until the glue dries.