Wiring subpanel in detached garage
A 125A &quot;main breaker&quot; in the subpanel is fine.
However, the breaker feeding this, which is in the main panel, must be 80A or 90A depending on the insulation of your wire.
Actually, I'd recommend a &quot;larger&quot; subpanel than 125A.   The thing you really want is spaces, because a 90A subpanel can support a whole lot more circuits than you think it can.   A whole lot more!   A 30-space sub would not be excessive, and ones with that many spaces will tend to be 200A.
The old &quot;16 spaces 32 circuits&quot; trick doesn't work anymore, since almost all circuits these days require AFCI or GFCI breakers. NEC 2020 now requires it for 240V loads.
If you thought &quot;125A breaker in the main panel is OK&quot;, then the source of your information is extremely poor - that's a hard mistake to make since every internet source will tell you otherwise.  Revisit every one of your decisions which came from that data source.
Other than that, everything sounds OK, but 125A on #2Al is such a blunder that you should really go through the rest with a fine-tooth comb.  Feel free to make full use of us!