Regression in [0], however the primary purpose of that code was to
cycle away from the active object (behavior which was intentionally
removed, see: T96752).
This broke weight-paint + pose-selection (Ctrl-LMB)
when the GPU depth picking preference was disabled.
Causing selection to pick the mesh object instead of the pose bones.
This de-selected the armature, making the pose bones unselectable
instead of selecting the pose bone as intended.
Adding the old code back (restricting it to weight-paint mode)
fixes the bug but reintroduces fairly involved logic unnecessarily.
Instead, prioritize bone selecting when in weight-paint & pose mode
(previously this was only done in pose-mode).
[0]: b1908f2e0b
3d72c37f7a