System Information
Operating system: Windows-10-10.0.19041-SP0 64 Bits
Graphics card: GeForce GTX 1650 SUPER/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 457.51
Blender Version
Broken: version: 2.93.0, branch: master, commit date: 2021-06-02 11:21, hash: rB84da05a8b806
Broken: 2.92
View Settings
Exact steps for others to reproduce the error
While I haven't checked your file yet, this is a most likely a floating point precision issue due to the large clipping range. It makes checking of the Z-values problematic. Always avoid using such big clipping ranges.
I tested with bigger Clipping Start value and found another strange issue with drawing the lines in Viewport.
Bigger Clipping Start range did not change Circle selection behavior, also lower Clipping End did not change behavior.
And I just noticed that it affect all types of selection (Box, Lasso), so bug report need to rename to somethings like
"Selection do not selects in X-Ray mode with close range to elements"
Bigger resolution to better see the issue with lines in Viewport.
This is caused by part of the edge being behind the view, causing 2D projection to fail.
One possible solution to this problem is to clip the edges by the near-plane before projecting into screen-space.
It may be necessary to clip by the 4 planes defined by window bounds as well - to prevent points near the clip plane being too large or infinite - causing other calculations to fail.