In theory the .ts files, if they have been decrypted by the copy to external drive, could be uploaded to the Aura. They may also be playable by connecting the external USB drive to the Aura and using VLC. If they won't play with VLC it may be worth checking the file(s) with ffprobe or MediaInfo. If they report no video/audio streams they are either encrypted or corrupted.
To copy playable files to the Aura's internal drive is more complicated. See
post #4 above.
"copy them back" suggests to me that you would like the full experience you had with the recordings on the previous Humax. You won't get this. If you are lucky you will be able to play them in the same way as a YouTube video or your own camera recordings. No stored summary and you'd have to use VLC or similar.