I think the question is now: was there more than one Western Brigade? And if so, which regiments belonged to it?
I don't recall ever coming across any other Western Brigade than the Iron Brigade of the West. I could be wrong about this. The other notable large command which came from "western" states and served in the east were the Kanawha Brigade (and later Division), which consisted of Ohio units. The 11th and 12th Corps each had a brigade that consisted almost entirely of Ohio regiments, but neither were purely western brigades. A Western Brigade in the West seems unlikely, as it wouldn't be notable.
There appears to be no association between the 24th Michigan and the 21st Ohio. The 24th organized in August 1862, received assignment to the Washington defenses in October 1862, and joined the Iron Brigade in November 1862, serving with that brigade until February 1865. After that it served in a series of non-combat roles, including the escort of Lincoln's body, until mustered out on June 30, 1865.
There were two 21st Ohios. The first was a three month regiment that served briefly with the Kanawha Brigade before mustering out in August 1861. It therefore could not have served with the 24th Michigan.
The second 21st Ohio was a three year regiment. It mustered in in September 1861. During the 24th Michigan's muster in and pre-Iron Brigade service the 21st Ohio served in the Army of the Ohio and saw active campaigning in Tennessee. It spent its entire enlistment in the Army of the Ohio and Army of the Cumberland, mustering out July 25, 1865.
For details, see
here.
As I said earlier, I checked out the 24th Ohio and 21st Michigan, on the off chance that somehow the regimental numbers got flipped. Both served with the Army of the Ohio and Army of the Cumberland, but appear to have been in separate commands throughout the war.
In AACW, there were several problems with the elite units that appeared by script. For example, the Philadelphia Brigade appeared twice (once as the California Brigade, and later as the Philadelphia Brigade). Since the Western Brigade in question appeared in AACW as well, and there appears to be no historical basis for it, it is likely that it is a holdover from the early days of AACW or was included to provide balance.
"Thank God. I thought it was a New York Regiment."- Unknown Confederate major, upon learning he had surrendered to the 6th Wisconsin.