Copy layers from one Comp to another with difference Aspect-Ratio

Based on how you are currently working:

• After you complete your motion design at 1080-by-1080 and get client approval for the 1-by-1 version, duplicate the Comp and change the Comp size to 1080-by-1920 and adjust as needed. 
• After you complete your motion design at 1080-by-1080 and get client approval for the 1-by-1 version, change the Comp size to 1080-by-1920, copy the Layers, then change the Comp back to 1080-by-1080.  If needed, use the Advanced tab in the Composition settings to adjust the Anchor option when changing the Comp size.

Consider working at 1080-by-1920 first, knowing that you will crop down to 1080-by-1080 later.

I typically need to deliver 1920-by-1080, 1080-by-1080, 864-by-1080, and 608-by-1080.  For this, I design the 1920-by-1080 first with artwork being able to “float” in mind and then crop down duplicate Comps - nudging Layers as needed.

If the vertical needs to be 1080-by-1920, I design at 1920-by-1920, again with artwork being able to float as needed when that is cropped to 16x9, 1x1, and 9x16.

When I design something like this, I always start with a comp that has the highest resolution the client needs—usually 4K. If the editing is going to be done in Premiere Pro, I use that master comp and the Essential Graphics Panel to create some expression-controlled menus and sliders to reposition the elements on the screen, change the size and even the timing, and then create a MOGRT. Then, in Premiere Pro, the video footage is dropped in a sequence with the desired aspect ratio, sized, and edited for the most effective story based on the aspect ratio (it makes a difference in how you cut and frame). The final step is adding the Mogrt to include the graphic elements, and the menus and controls are used to match the graphic position and even the timing of the edit. I do this because editing video in an NLE is always faster than in After Effects unless you need to apply effects and composites in each shot in the project that cannot be added in an NLE like Premiere.

Chat GBT gave you some pretty amateurish advice. 

Step 1, adding a null and then copying and pasting, will do no more than Pre-composing except take more time. Neither is as efficient as creating a comp at the highest resolution, rendering the comp, resizing the render to fit the different aspect ratios and then rendering a resized copy because you save render time. However, none of those approaches consider the framing, timing, relative positions, and even timing issues you should consider when you design for different aspect ratios. 

If you are going to do all the work in After Effects, I would start with your master comp at the highest resolution, get the project working well and approved if needed by the client, then duplicate the master project in the Project Panel, resize the comp to the other required size, add as many nulls as needed or pre-compose as many layers as necessary to move and scale elements in the design to make the project work as well in the new aspect ratio.