I've found a lot of people asking this same question at various points in the past, but I haven't found a single real solution, and I've been stuck on this issue for days.
I'm just trying to export an FBX with multiple objects in the scene.
Unlike most 3D software, Houdini is dead-driven to always combine the scene into a single object on FBX export. I absolutely cannot find any way around this.

There are a lot of reasons someone would want to do this, but my current issue is that I need separate objects to properly bake the maps in Marmoset Toolbag, since I have intersecting geometry. It's similar to the “Bake by Mesh Name” in Substance Painter.

Have you tried adding every geo container to a Bundle and exporting it?

I didn't know Bundles existed. I figured out how to use it by looking over the documentation and made the Bundle successfully. But for some reason when I try to export the Bundle as an FBX, it results in an empty FBX scene. When I open it, there's no geometry inside, and the file is extremely small.

Here's an image of how I have it all set up;

This got a bit more strange.
After some experimenting, I found that I could get the geometry to export successfully if I jumped to the highest level and only added Geometry nodes to the bundle, instead of nodes inside the geo like I had before.
Normally that would be the end of it, except that doing this exports ALL the geometry nodes. Even ones not included in the bundle.
Or rather, it creates a bunch of extra null objects in the scene for anything not included in the bundle.
And this only works if I actually try to export the bundle, despite it including things NOT in the bundle. If I try just exporting the geometry directly without the bundle, it creates another empty scene.
If I select one specific geometry node to export like before, then it successfully exports that one piece.

-Edit- YES! I've found a solution. Hopefully there's a more straightforward approach, but for now this does work.
So I had to use a bundle, and only fill it with top-level geometry nodes as I first described. Then to prevent it from creating a bunch of null objects in the scene, I have to right-click every node not part of the bundle, go into Flags, and set it as “Hidden”.
This absolutely should NOT be necessary, since the Bundle should already be isolating these out of the export. But it doesn't, and this does fix it.
Of course, it shouldn't even be necessary to use a Bundle in the first place. But export by pattern (selecting multiple objects) is a non-functional option which just results in an empty scene.

Yeah, you gotta pay attention to that “Export Invisible Object” dropdown in the FBX ROP, several gotchas to be avoided depending on what you set.

I mentioned bundles but I also believe you can just group every Geo container you want to export into a Subnet and point to it in the fbx export ROP and it will export every geo in one fbx files but as separate objects. I think the scale of the Subnet node is also taken into account iirc. So if you work within houdini and everything is too small in centimeter-set packages after import you can just put 100 in the subnet scale.

Edit: I just noted you are exporting separate pieces in the obj-level. I actually only tried bundles to group scene-level geo containers, good that it seems to work though.

Ah, yeah. I tested adding the geo nodes to a subnet, and it worked. I think this is the best approach so far. The only issue is that it creates a single “world” null object. But having just one empty object in the scene isn't a problem.

A little late, but I found out you can get rid of the useless null object by just unchecking “Create Root for Subnet” underneath the Source Objects when exporting. Everything now works perfectly.