If you have more than 30 medals and you switch from the Premium Plan to the Basic Plan in the mobile device version of Pokémon HOME, any medals beyond the 30 most recently received will no longer be available for trading or gifting. The medals themselves will remain stored in the app.
Under the Basic Plan, you can view up to 30 medals in the Basic Box screen. For any others, only the total number will be visible and detailed information will not be accessible. If you upgrade back to the Premium Plan, you will regain full access to all medals, and you will be able to trade or gift them again.