If you use long enough lags to get a good bite into the stud, your first proposed method should be fine. If the "lever" action is high enough to snap a lag bolt, then it will be strong enough to snap the 2x3 as well.
From a strength perspective, it doesn't matter how long the lag bolt is - the torque and shear at the junction of the wall/bracket interface is all that matters. It doesn't matter if the lag bolt sticks out 3" from the wall, or if just the bracket sticks out 3" from the wall. You get the same torque applied from the same downward force if you assume the lag/bracket/mantel assembly is one rigid body. And if it's not, then something internal in the shelf has already failed, and you don't need to worry about the torque loading on the lag at the wall.
If you wanted to use shorter lags for some reason, you could always countersink them by drilling into the 2x3 with a bit larger than the lag head.
When the two members are not touching, the bolt starts to act as a "cantilevered beam" (as you have alluded to) and you hit a point where it is not the shear value that governs, it is the moment (bending). You get additional support by the cleat trying to go down and into the wall which puts withdrawel load on the fastener effectively adding more support using the tensile strength of the fastener.
As a note standard zinc hardware store bolts are ungraded steel usually with no actual values assigned to them.
First, if you have the time, you might try to buy some graded bolts online or from a local supplier; not necessarily a high grade, just graded at all so them meet a minimum requirement for strength. Or use structural screws such as Simpson SDS screws.
Secondly, if you have effectively 1-1/4" of cantilever, I would recommend slightly more embedment into the stud. If you hold things flush to the wall with only a 1-1/4" cantilever, I would up the embedment to a minimum of 2-1/2" or more to ensure the wood stud does not crush at bolt under load due to the multiplying effect of the cantilever. Visualize a 12" long bolt embeded 1" in to a 2x4, the wood crushes on the 2x4, the hole enlarges, and the bolt comes out; the bolt does not necessarily even bend before failing. An increased embedment also increases the amount of withdrawal load the fastener can handle when it slides down the wall (if the bolt does bend) and tries to pull out.
Another option is to simply get more fasteners per stud. You can do this by upping the size of the cleat to a 2x6 and use two or three bolts. Or you can add a vertical member below the cleat at each stud and effectively add a bolt every 4" or so in the vertical member with predrilled holes plus the bolt(s) into the cleat. Key is more embedment and/or more bolts to handle the cantilever.
Or, just build them free standing.
Best Answer
You do not need to be concerned, assuming that your lag screw is anchored into the framing.
That's a result of a pre-existing gap behind the drywall. Maybe some insulation or a wrinkle in the vapor barrier held it out during initial hanging, and your lag screw pulled it in tight. Because there was a drywall screw there holding it out the surface bulged as the rest pulled in. There are no apparent structural concerns.
If you ever remove the tv, you'll want to put a pair of drywall screws above and below the bulge before removing the lag screw. Then remove the tv mount, cut away the bulged drywall and repair.