White isn't especially useful for beveling if you have a white background. But if you also have the dark side and the background isn't totally white, it's worth a try. I put a grey background to see all well in this demonstration.
You can also use something colored instead of white, if it matches with your art.
A test shape, resembles a little one of your shapes. Lets call it "Shape" here.
make a copy of Shape, no fill, solid white (or black) stroke. Actually you need total 3 versions of Shape. Lock and hide those which aren't under work. Use the objects panel for easily controlled selections.
With the node tool insert some nodes. You must have a node in every place where dark and lighted bevels fade to each other. Select those nodes, in the node tool info bar click "Break path at selected nodes". Confirm it with Path > Break apart.
- Recolor the path segments to bevel shading colors. Group them.
5.Insert (=unhide) a copy of Shape, lower it to the bottom
Blur the bevel group
Insert a copy of Shape to the top, select it and the bevel group, goto Object > Clip > Make to remove the exessive blurred bevel.
You can reduce the blur, increase stroke widths or duplicate the bevel group to make it stronger. Grouping and the clipping mask do not prevent selecting and editing. Beware: You can easily get totally lost if you accidentally move something to invisibility under the clipping mask.
Here the bevel group is duplicated:
Blurring may not be a good idea, if you want to make a general SVG export to another software. Here's an alternative. It uses gradients:
Bevel area is divided with the node tool to segments differently. Black is the shadow, green gets transition gradient from shadow to light and the cyan will be the light.
In the middle the bevel coloring is done.
In the right Shape copy is added to the bottom and another copy has been used to clip the grouped bevel.
The result hasn't the rounded appearance of the blur.
Add due a comment:
Inkscape effect support varies in other software - Blur isn't an exception:
This is drawn in Inkscape 0.92.2 - a rectangle and a copy with blur:
this was saved 2 times - as Inkscape SVG and as a general SVG. Both opened in Inkscape ok.
Both opened in Illustrator as follows:
Illustrator is a pre-CC version. New Illustrator can be better.