Hmmm.... I have to admit something now: I can reproduce your issue! It staggeringly fails from within the Pro interface with the error message you show. ;-() This is one h*l of a bug.
What were my remarks based on, you are asking? Well, I have been debugging an arcpy based application that needs to run in both ArcMap and Pro. That application routinely saves layer files with spaces in the filename through arcpy, using the following statement:
*** This works in Pro for saving layer files with spaces! ***
inputLayer.saveACopy(newLyrFilename)
I have never seen this command fail, and have run it in batch on hundreds of layer files... I can save and load layer files with spaces fine through arcpy using this and other arcpy statements. Loading a layer file with spaces manually from the catalog window by drag-and-drop is also no problem, I have done that dozens of times in Pro.
For some reason though, I just didn't save them from within Pro manually, as my main focus for the development of the layer files has been ArcMap, and I simply upgrade them to Pro using the above shown command in an automated fashion. That is why I totally missed this issue, despite regularly having tested stuff in Pro!