Files are files and filesystems are filesystems. You keep your files on filesystems.
NTFS and ext4 are non convertible - you cannot turn one into the other directly, in place. However you can take files from one and put them on another.
Yes, moving TBs does take time, sorry it is unbearable.
Rustdesk is pretty decent and being developed quite fast. Why not look at MeshCentral too. Choice is good and MC has been around for a fair old while.
My company replaced Teamviewer with MC and we have thousands of client machines across the UK.