Thanks for the context, Justine!
+1 to the suggestion to reply directly. Get a template in place so it's an easy copy + paste for these instances. It can definitely be a more human response to set expectations and explain why they're being pointed to another channel. If you notice repeat offenders you can also consider temporary bans (if it's in your CoC).
I know we're in a CMA channel so community might not be your full time role and you might not have the bandwidth for these next suggestions. I would take this as a signal and...
think through hosting community office hours where I partner with support or CSC to join 1/month and answer questions (think reddit AMA or webinars).
think through an automation to create a support ticket from Slack (the members don't care about your org structure, they just want help on their question and this is a step in that direction).
think through my current rituals on the Slack community. Do I need to lean more into content and events so there's something more appealing for members to be in the Slack for? Are they coming here for support because the other things happening in the Slack aren't as attractive.