Your device will probably play aac files your problem is most likely being unable to connect to the server, both the links you say won't play are hosted on the Amazon Cloudfront server.
That is the limit of my knowledge about servers so I can't say whether there is a way to connect or not.
I have a sketch that allows me to play various files from a SD card to a vs1053 using a Nano ESP32 and I know the aac format works in that situation.