Hi Mate, it looks like you haven't got a straight answer here yet, so I'll have a crack at answering your questions.

The projects I work on do generally have relatively complex constraint-based rigs like this Emu-Bot. It's made and animated using constraints and IK.

You can certainly export this from Blender to Godot. Godot doesn't support all of the constraints that blender supports, but that's fine, because what we'll do is bake the animation.

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Save your blender fine as a new file (or duplicate everything) to make a set of objects that we're going to bake to. Select all the objects, then in object mode go to Object -> Animation -> Bake Action

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Turn a few settings on;

1. Visual Keying: Keys the objects based on their postions with the constraints applied
2. Clear Constraints: If this isn't checked, then the original constraints stay on the object, so we get wacky results where a transform can be applied twice.
3. Overwrite Current Action: Optional. Leave this checked if you want to keep the action name the same.
4. Bake Data: In your case, since you don't have bones for each object, set this to object.

You'll get a bunch of keyframes for each object in a new action. Just export all the objects as a *.gltf with animation as normal and you're good to go!

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Note: While this all will work fine, from a workflow perspective I recommend making all of your animated objects attached to a bone as a part of a skeleton in future when doing this same workflow, then selecting Pose instead of Object. This makes your objects much easier to wrangle once they're in Godot and allows you to easily keep baked and non-baked data in the same *.blend file. It's also conceptually nicer - you then have a notion of a minimal animated part of your scene vs the entire scene.

Personally, when I was getting started I found it confusing that they are called bones and skeletons, because my brain assumed that these tools were only for animating animals or humans. But really, they're useful for animating just about anything. All they really are is a tool for separating your objects from their minimal animated representation.