So take this with a grain of salt (bc I've never freelanced) but I've been the busy client, and I'd say it's totally fair to set the expectations you did in your OP.

You could even add something like "it seems like you have higher priority work happening and things are a little busy— I totally get that! Just let me know if you need any more work from me on this project (or any others in the future), as I have other clients who want to increase my hours, and I'd like to get back to them on my availability. I've re-attached the invoice here."

Might come across as blunt, but tbh it helps to remind your clients that your time is in demand (even if it's a little white lie). It could push clients like this to just figure their shit out.