How to split a model in SketchUp for printing
SketchUp is likely to not work well for you if your objective is to create a printable STL file in pieces. You would want to determine initially that the un-segmented model is manifold and 3d printer ready. Once that is determined, consider using an alternate program for your chop-up actions.

You do not specify the size of the printer you intend to use, but that is obviously a factor in the segmentation of the model.

I have some experience with Meshmixer, which has an edit feature named "plane cut" which will do as you require. The plane is placed on the model and the options are selected to keep both pieces after the slice is performed.

For a huge model of the type you describe, one would hope you have access to a printer with a one meter print bed or larger, although such printers are rare and of course, expensive.

My printer has a 200 x 300 mm build plate, up to 200 mm high, which would entail substantial segmenting.

If your model is mostly a shell, your segments would have to have wall thickness. It would be best accomplished, again in Meshmixer, by using the hollow or shell features. Those are a bit more challenging to understand, but there are plenty of videos and tutorials specific to creating hollow shells from a solid model. Once the shell is created, segments would be managed easily enough.

I suggested that your segments would "have to have" wall thickness, but it isn't a requirement. Solid segments would be like bricks and you may have a large number of rectangular solids that compose your model. Lego models are difficult or impossible to create with only an outer shell, so the interiors are often solid bricks, but 3d printers are a bit more flexible. Not using solid interiors would save money, of course.

I envision a jigsaw puzzle in three dimensions. Taking a nearly six meter dimension and chopping it into 20 slices multiplied by width and height means a carton of 3d puzzle pieces.