Resizing Ubuntu partition with resize2fs

The problem you're having is shown by the output of lsblk:

gab@someserver:~$ sudo lsblk
NAME    MAJ:MIN RM  SIZE RO TYPE MOUNTPOINT
xvda    202:0    0  5.9T  0 disk 
└─xvda1 202:1    0    2T  0 part /
xvdb    202:16   0  1.8T  0 disk 

/dev/xvda is 5.9T, but /dev/xvda1 is only 2T. You need to first resize the partition, and then you can resize the file system to the size of its block device. Since the file system is on /dev/xvda1, that's why resize2fs is saying "nothing to do". You need to use a partition tool, such as fdisk, or parted, to change the size of the partition for you.

On Google Compute Engine, this is actually done automatically for you. When you grow the size of the Persistent Disk (GCE's analog of AWS's EBS, if the VM is running, it will automatically resize the partition and the file system for you. If the VM is not running, it will happen automatically when the VM is booted or when the PD is attached. (Disclosure: I work for Google.) I thought AWS did the same thing --- perhaps it's because you're using a very old version of Ubuntu (16.04 is six years old and it's End of Life was in April 2021) and AWS never updated its daemons to add this feature to 16.04? I'm not sure.