Would it be possible to make the column widths in Layer Manager adjustable (or auto-fit something like like Excel columns)? Then, make the adjusted column widths persistent so that when a particular project is re-opened the column widths are the same?
An alternate could be to make the Layer Color, Line Style, Line Weight, and Display Priority columns "auto fit" and the Layer Name and Group Layer adjustable.
I notice also that the "Protect" Column heading is truncated because the column is too narrow by default to show the full word. (Although this might be a 4K monitor issue?)
No panic, just a thought