Hi and thank you for accepting me in your group!
Is there a script to use only the cross-section system of the Blender-BIM add-on, within a normal .blend file?
I think that since the whole BlenderBim add-on relies on the IFC schemas and ecosystem you can't really take advantage of the tools without actual IFC elements and drawing parameters. You didn't specify what your actual needs are so it's a wild guess, but you can try out the default Bisect tool in edit mode. You can use it on multiple objects too.
(It's bugging out at the end because Suzanne's mesh is non-manifold)
Is it possible to select and object, which creates a sectioning Bounding Box around the object?
Yes indeed the BlenderBIM Add-on's temporary section cutaway feature works on regular Blender meshes and actually has nothing to do with IFC. The only caveat is that it works using shader tricks, so you have to be in material preview or rendered viewport mode to see the results. It also therefore relies on normals being correct.
To create a section bounding box, just create multiple sectioning planes. All planes are independent and you can have as many or as little as you want. It might be a nice feature to build a tool where you can create a sectioning box with one click, instead of the 10 clicks it takes right now.
You may use collection boolean feature in blender 3.0, basically using whole collection as operand and simple box as cutter. While slower than shader trick, it will provide support for shadows.