What role does depreciation play in break-even analysis based on accounting
flows? Based on cash flows? Which perspective is longer-term in nature?

Depreciation has no effect on cash flow analysis other than its effect on taxes.

Break-even analysis is much less formal, so whether you include it is
up to you.  Most would not include it, because to put off the payment
into the future may render you insolvent in the meantime... which
means you wont get to that later point.