still don't know if I should mention the counteroffer from my current job during salary negotiation

Got a counteroffer email from my current manager the same week I was supposed to negotiate an external offer, and I genuinely don't know if bringing that up helps or just muddies the conversation. Part of me thinks it's leverage, part of me thinks it reads as using one company against another in a way that could backfire. Haven't sent anything yet, still sitting on both emails.