For a cold email system that relies on paid platforms like Instantly, should I cover those platform costs by charging the client a small monthly maintenance fee, or should I have the client pay for the platforms directly?

There's only a minor difference between the two — either works. If having the client pay directly is a limiting belief for you, just get them to pay you instead. But the benefit of having the client sign up for the platform themselves is affiliate revenue: you can get a cut of their Instantly signup (e.g. 30-40%), so if they spend $100/month you've effectively made yourself an extra $40/month, plus there's perceived value in being a platform partner. I personally prefer having the client own the whole tech stack and sign up directly, mainly to avoid liability — when a client inevitably stops working with you (it happens a lot), you don't want to be stuck handing off usernames/passwords for tools you're sharing. Yes, it takes a bit longer to onboard since you have to walk them through signup on a kickoff call, but it eliminates that handoff problem entirely.