Best way to backup/restore a very large DB (~2TB)
You may need to think further ahead -- When reloading, will you have enough space?

Setting innodb_file_per_table does not necessarily provide any extra space.

When you do SHOW TABLE STATUS;, the "Data_free" will indicate how much free space there is in ibdata1.  How big is that?  If it is small, then something more needs to be done.

Is it possible in that OS to "extend" your current drive with one of those spare drives?  That is can you, with an OS command and without dumping, extend the current "drive" to 4TB?  If so, that is is probably worth doing to get started.

If you do backup, it will need to be to some other drive, either on the same server or on another server.  (That is, do the dump across the 'network'.)