I am trying to specify a rectangle width of 10,600 pixels but the geometry settings box is limited to 10,000 pixels. I can drag the sides of the regtangle to be larger than 10,000px but the displayed size cannot show any size greater than 10,000px. Any workaround?...

When you create a rectangle (vector or paint layer), the Tool Options docker has settings that let you set the size to greater than 10,000 pixels.
So, the 10,000 limit for vector properties adjustment looks like a bug. (No workaround as far as I can tell.)

Please report this at https://bugs.kde.org/ (Account creation and login are needed.)
Also reply here with a link to the bug report that you create.