I’ve noticed that using the APR button in most MSFS aircraft doesn’t work at all if the LOC isn’t immediately changing from white (armed) to green (captured).
If you are flying on an intercept heading with LOC and GS in white, the aircraft will continue on its present heading and altitude.
A few miles too far out and I need to use NAV/LOC.
Once the LOC is being captured, pushing the APR button will correctly intercept the ILS.
It’s not realistic, but that’s the way you presently have to use the AP with e.g. the MSFS TBM.