Hello - I just purchased the new MacBook Air M1 and I am getting the impression I have to pay for Apple Music to get access to all the music I have ALREADY purchased through iTunes on my old Mac. I REALLY hope this is not the case !

You do not have to subscribe. Apple just likes to present you with the opportunity every waking moment. In fact the really smart user makes sure that they have all their media backed up on several drives so you you don't even need to rely upon re-downloading music from Apple. If you read the terms and conditions it says it cannot guarantee your past purchases will always be available for re-download.

http://www.apple.com/legal/internet-services/itunes/us/terms.html - "It is your responsibility not to lose, destroy, or damage Content once downloaded. We encourage you to back up your Content regularly." ... "Content may not be available for Redownload if that Content is no longer offered on our Services." And: https://support.apple.com/ht204930 - "Apple Music is not a back up service, so make sure to always have a back up of your music collection before you make any changes."