Nope! I just updated to macOS Big Sur 11.2.1 and it's only partially fixed.
In the Save As dialog I noticed that while it now continuously retains the resizing of the main right-hand window pane (folder and file list), the Sidebar window (locations, favourites, tags...) reverts back to the extremely annoying small default size on any subsequent occasion when no resizing of the Sidebar has since been made.
For instance, every time I resize the width of Sidebar window in the Save As dialog and then exit the dialog (using Cancel or Save), it will retain the new width size on the very next occasion the Save As dialog is launched - giving the impression the bug has been fixed! But... if I exit the dialog as is without making any further resize changes to the Sidebar window it then reverts back to the small default size on the very next occasion.
I actually can't believe Apple with their top-quality software developers manages to get this half-baked fix pass quality control before the update is deployed.