How to split a catalog into several smaller catalogs without moving the original images?

I have well over 350,000 images in my 10-year-old Master Catalog and have experienced no performance problems related to its size. The catalog file size actually grows quite slowly, and as long as it is backed up in more than one location, I know of no reason why it should be split into smaller catalogs. 

Export or clone your catalog, then remove the images you don’t want from the new catalog.

To answer the question asked, there is no way provided to split a catalog directly, but you can still achieve the same effect in a few steps as below. Let’s stipulate there IS some organisationally and practically sound reason to do this - leaving aside the reasons suggested in the OP, which don’t make sense to me personally. Say, you later decided to separate paid work from personal photography.

I strongly recommend a Catalog backup first, also ensuring images are backed up safely, both into separate hardware from the working setup.

Then you can in one step create a new catalog which includes only highlighted images from the current catalog. Those images can have been selected in any way you want, by their folders or otherwise. The command is “Export as Catalog”. This has some options. One of these is “Include Originals” - uncheck this, so the image versions in the newly made catalog will refer to the same files, in the same places, as they presently do within the current catalog. Checking this would have copied them alongside the newly made catalog. Another option is “Selected images only” - check this, otherwise all the images would be exported regardless.

The outcome is that a separate catalog now exists (under the name and location you chose) which contains - in full functionality - only the chosen images. You still have got your current catalog open, with all those images you chose before, still highlighted. 

One keystroke can Delete all of these BUT make sure to use the option Remove from Catalog. The referenced image files must not all be deleted from disk of course, since this other catalog you have just created, now has its own separate dependence on those files.

When you open this other new catalog those images appear just as they did in their prior home: virtual copies, stacking, latest edits and prior edit history, collection memberships; and in the same context of smart collections, keyword list etc.

You haven’t presented a good reason to split your catalog, there is absolutely no problem having some photos on a laptop and the rest on an external drive.

So my advice to you is don’t split the catalog. I don’t see a benefit.

There is no reason to export anything. Just make a copy of your catalog, let’s call them Cat A and Cat B. Now open Cat A and remove all the photos that you want to be in Cat B. Just remove them from the catalog, not from disk! Then open Cat B and remove all the photos that you want to be in Cat A. That’s it.

OK first, is there a good reason why you are splitting the catalog? Because of some specific issues with how Lightroom Classic handle catalogs, managing images across multiple catalogs is significantly more awkward, challenging, and time-consuming than maintaining a single large catalog. Also note that catalog size does not directly impact performance. 

I have tried to split the archive off by using Export Folder

Which command are you using exactly, because I don’t see an Export Folder command. 

If you selected a folder and then chose the command File > Export, then you are exporting copies of the images, and it sounds like that is not what you want to do. If that command asks you for a destination, it’s for the copies of source images. 

If you’re trying to split the catalog, then you should be selecting a source (folder or collection) and then choosing the command File > Export as Catalog. It will ask you for a destination, but that folder is for the folder where you want the new catalog file to be; images are not involved yet. When you use File > Export as Catalog, source images are not copied unless you also selected the option “Export Negative Files.”

So if you want to specifically do this…

How can I split a catalog into 2 with selected folders in each without moving the actual files?

…then:

1. Select one or more sources/images. 
2. Choose File > Export as Catalog, and set the destination of the new catalog you are creating. 
3. Do not select “Export Negative Files.”

That will create a new catalog, referencing only the sources that you selected, and without changing the location of the source files.