Arguing over definitions is not useful.

Arguing over definitions is foundationally necessary to discourse. If we cannot agree on what terms mean, communication is impossible.

Maybe distinguish between two distinct notions of Peak Oil,

When you capitalize Peak Oil you are invoking the body of rhetoric, lore, and history associated with the term. That term has a specific meaning, which invokes a catastrophic economic failure scenario derived from discussions of Hubbard's Peak.

Note that from an economic growth standpoint definition 2 might still be a cause for worry even if one doesn't think that there will be a definition 1 type of issue

Hardly. Economic growth under sufficiently stable conditions is inevitable. Furthermore; that oil production will decline over time is inevitable. The only question is whether it will do so sharply and in a vacuum of other solutions, or if it will do so as a part of a pattern of transition to other avenues of energy production once it ceases to be the most viable source of energy production (which, honestly, it isn't even that; coal is. Which is why we burn coal for electricity and not oil, but I digress.) The answer to that question is unequivocably that there won't be a catastrophe.

So "Peak Oil" is nonsense. That oil will peak and production will fall is insufficient to proclaiming "Peak Oil".