Prior to to the braces, the columns would have bent inward as they took load. After adding that brace, they will move in an arc around the point where the brace is attached to the wall. (Assuming the wall doesn't move.)
Here is a sketch of how everything would move together:
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A very nice sketch wissix and I do appreciate your concern for my safety. Your sketch did leave out the top cross bar however and that is significant. Noticeable movement at the top of the columns does not have to occur nor is it desirable. It can and does occur because many lift companies have cut materials cost and are meeting minimal design standards driven by price point. A simple support has helped mitigate this cost cutting and allows the lift to feel like a much more rigid structure.
Right. Other things have to give, which is more the worry. When the load goes up,
something has to move. The walls weren't designed to have a truck hanging off the side of them, so they would (could be a small amount) deflect inward. (Besides the question as if they can take the load, that inward movement can also stress the ceiling above.)
I would be cautious adding a second brace without working with a structural engineer. In your current state, your post column can move with the wall and the two can arbitrate the loads a little bit. If you add another brace and have them forward and aft, then the wall will share 100% of the loading with the post column. (But the column would move straight inward with two braces.)
The load is fully supported on the columns. Not shared with the wall. The wall simply stabilizes the columns. The bolts in the floor do their job. All I'm doing is offering a bit of resistance to deflection fore and aft and dampening vibrations induced by load movements.
One thing you might do is the next time you take a load on the lift, check the plumb of your columns before and with the load at height and see how far they are rotating backwards towards the braces. (Maybe even measure from the back of your garage to the top of the column before and after.) The movement may be very small, but if you noticeably fall out of plumb, that would be a greater concern.