May depend on what the object you want to split is. If it is a single path you could use the line to [path] [cut path] then rejoin the end nodes with a line and refill with color.
Another method - make a rectangle that covers more than half
- make a duplicate and drag that to let them snap side by side , then group the two rectangles
- bring your target object to the top and then do your alignment with the group. then ungroup the rectangles.
- make a copy of target object with [edit] [copy]
- select target object and one rectangle use [path] [intersection]
- use [edit] [paste in place] then repeat above step with the other rectangle.
- recolor the two halves back to original.
Looks like this before splitting. The red being a representation of object to split.
View attachment 997690
May be other ways to do it as well.
Edit: I just had a play. after the alignment in the above steps. Delete one rectangle. Then select target object and push it underneath. Then you could use the [path] [division] to split in half keeping original color.