When did Apple start charging a subscription fee to access my paid for downloaded music?

Could you have accidentally bought an Apple Music subscription by mistake when trying to play/find your originally purchased music? I haven't heard of anyone having to pay to access the content they have previously bought before.

You can view and cancel your subscription following the steps at How to cancel a subscription from Apple – Apple Support

You could potentially try and claim a refund by contacting Apple's Form > Request a refund for apps or content that you bought from Apple – Apple Support however this isn't guaranteed and it is up to whether Apple allow the refund or not.