Hi Joe,
Thanks for the feedback and providing links.
Instead of copying the layout you may want to consider using Layout files—ArcGIS Pro | Documentation . These act as a template for layouts. You have an option to create a layout file with an empty map frame which you can then use to populate with a new map. I you decide on using layout files I recommend reviewing the blog post Customize your layout gallery (ArcGIS Pro 2.5).
Unfortunately, when a map frame is empty ("<None>") legend properties are set to the defaults. However, you can save the properties for a legend item as a new default (hopefully we'll have something similar for the legend as a whole in a future release). This will be the property set for any new layer added to this legend or any copies of this legend (either copied to a different layout or included in a layout file). For example, if you use a different font than the default for item labels (ex: Stencil) and you save a new legend item default any new layer added to the legend will use Stencil as the font for item labels. This will also be the case if you point the map frame to a different map, or even if you empty the map frame.
For more info see Work with a legend item—ArcGIS Pro | Documentation. There is also a good blog post you might find useful - Tips and Tricks for Working with Legends in ArcGIS Pro.
Another option would be to copy the legend (with all the formatting) from the original layout into the new layout. Update the map frame source in the legend properties as needed. You may need to change the map frame source to "<None>" and then back to the map frame proper to refresh the legend.
Unfortunately there is currently no way to have different versions of a single map (ex: one version with a layer on, a different version with the layer off). You will still need to have different maps. Of course, if time is of the essence and setting the default legend item and creating Layout files is not currently practical, the option you had in ArcMap is also available with ArcGIS Pro. You can make a copy of the project.
Hope this helps,
Tom