The F-Test: Detecting A/B Test Interactions and Conditional Treatment Effects

We needed a principled approach to help find heterogenous treatment effects and to discover if A/B Tests with more than 2 arms were potentially interacting with one another. Most approaches seem to just use single t-tests with multiple comparison adjustments, but this approach just became too unwieldly at scale. Anyone else use the F-test with nested regression? Or find some other useful approach beyond collections of individual A/B tests?