By sales I mean the specialists who communicate with clients before they receive services, retain them, lead them to purchase and all that. And support is when a client can reach out with questions, problems, difficulties and so on. Would it be a bad idea to have the same people handle both?

If it doesn’t overload the team, then probably yes. Honestly, I’m not very good at task distribution, and I’m pretty sure you understand your business better.

I agree that if processes are set up properly and there’s no overload, then a customer support team can handle both directions with the help of tools and clear scenarios. I would also consider outsourcing services and external teams that offer both sales support solutions and handling client requests after the service. It makes things easier, because you relieve your team without losing service quality.