Sorry to possibly throw a wrench in your plans.
I have exactly 0 experience in making an AI, but have been reading about various tactics in implementing things, as they look interesting.
I know FSMs (but in a different context), and browsed BTs a bit (and like you I have problems picturing its execution).
Recently I ran into GOAP (goal oriented action planners). In GOAP, you let go of rigid order in decision making, and instead have individual actions that you combine into achieving a goal.
I cannot tell you how this compares to FSM or BT, or even if it actually works, due to my 0 experience, but it sounds like this may be an alternative that could be of use, for some part of the decision making.
GOAP is really for high-level strategizing. It can be pretty smart, but it's really only good at selecting action states. For a game like Shadowrun it would be simpler, but in a top down squad shooter like OP describes it would likely be hybridized with an FSM or similar.