Thanks for the detailed report, and you’re right about 603.5! You can decline, just later than the targeting step. Choosing a target is required when the trigger goes on the stack (that’s why Cancel was grayed out). Then, when it resolves, the game asks “Use triggered ability of Foundation Breaker?”, and answering No keeps your Birthing Pod. I tested it and the question does appear.
If you didn’t get that question, you probably told the game to always answer yes for this trigger at some point (the Y key, or “Always answer yes” in the stack’s right-click menu). That’s remembered between games. To undo it, right-click the stack and choose “Forget what I have remembered”.