Is it normal for a command to require proof of a conversation with a medical provider?

That completely violates HIPAA. No one in the military is exempt from federal laws, especially HIPAA.
Tell your commander that his/her request violates HIPAA and if they believe it does not, they may request the document themselves from the therapist.
If they continue to insist, tell them you will comply if they issue the order in writing. Take that written order to your IG and there will be no more issues.

Conversations with your therapist are generally no ones business but yours and your therapist, with only a couple exceptions and your levy packet on the surface doesn't fit that bill (if you made some sort of allegation of misconduct by the command in regards to your packet then it may). Go see the IG or JAG for an official opinion on restricted communications and what you are required to share with your command and comply accordingly.
The command is however perfectly in their lane asking for appointment slips to account for your whereabouts and absence during the duty day.

a conversation with your doctor is private, if you are not comfortable you should not have to share that information in any way, i would check with JAG or IG if you cannot discuss it with the commander, maybe the commander just needs ammo to help/hurt your levy process. you know the commander cannot brief their commander with hearsay as evidence.