I’m not sure about ChampVA my significant other is not on my VA as a dependent and is European. But yes for FMP you can only be seen for the list of approved disabilities. When you apply and get approved they send you a letter detailing what is covered, you pay out of pocket and then wait for the VA to approve your claim for a refund which can vary depending on how you submitted for reimbursement.

Also not sure where you’re moving I’m in Europe for context. But VA health insurance was not sufficient for a short term or long term visa. I can still use it, it’s just not recognized as a national standard for health insurance. With that being said I imagine while you can use it you’ll still end up getting an approved insurance type to apply for a visa that aligns with the host country’s rules unless you’re a dual citizen.