Unable to transfer purchased iTunes songs from iPhone 5s to new iPhone

I had an iphone 5s for a few years and purchased over 900 songs from itunes to my music library. I did use maybe two different apple id’s but it was so long ago so no idea what the ID’s were now.Is there any way I can get these songs on to my much later iphone as I paid for every song and apple have made a lot of money out of me. I did call apple up but they said I needed receipts etc to show I bought them but surely once a song is paid for and downloaded, thats enough proof and the songs is mine! Im furious apple have ripped me off. The old 5s barely holds any battery now but all my treasured songs are on it.

Apple need to stop all this blocking business too. When I used to plug the phone into my laptop / itunes the songs all came up but there was no way to save them to that laptop or transfer to another phone. As soon as I disconnect the phone the songs vanished. I really want my songs I paid for on my new handset!!!!!

[Re-Titled by Moderator]