How the wedge works in my Colts:
I have 6 Colt revolvers that have the barrel wedge "feature": a Uberti 2nd Model Dragoon, a Colt Signature 3rd Model Dragoon, a Pietta 1851 Navy, a Pietta 1860 Army, a Uberti 1861 Navy and a Uberti 1862 Pocket Police. All work the same way.
The barrel assembly has a screw on the (gun's) left side, placed in such a way that the head of the screw contacts the wedge spring's upper surface when the wedge is in the barrel slot.
When the wedge is driven through the barrel assembly, that is, inserted left to right as seen from the back of the gun, the screw head depresses the spring so that the lip of the spring is lowered and does not interfere or contact the barrel assembly.
With the wedge fully inserted the spring is still depressed such that the lip on the spring is below the outer mold line of the wedge and thus fully within the channel in the wedge. It does not protrude above the wedge and cannot contact the barrel assembly or interfere with removing the wedge.
When the wedge is driven back out of the slot (removed), the screw head allows the spring to return to it's undeflected position as the wedge moves right to left. In the fully restored (undeflected or relaxed) position, the lip on the spring contacts the back side of the screw head and prevents the wedge from being fully removed from the barrel assembly. I believe this is the intended purpose of the spring, the spring lip and the screw.
This is a best a rudimentary design. Some degree of precision is required of parts that are subject to damage and wear, so it is to be expected that it would not work all the time. The spring can become worn or bent and loose restoring force, dirt can become lodged under the spring preventing it from being fully depressed, the lip can be worn down, the screw head can become nicked or bent, all of which will affect the design performance.
All of mine still work, but many people have difficulty with the wedge and wedge spring. It's not the best "feature" on the Civil War era Colts.
