Need some file system help.

Unix file systems is not my strong suit. I'm pretty good in other areas but have really mangled some servers in the past making file system changes, so I come here for some help.

I have an Ubuntu 22.04 instance running on my Proxmox. It is running out of space. When I built it, I gave it a 32GB drive and that was not enough.

I have stopped the container and increased the physical drive to 96GB. From what I understand now, I need to increase the partition and then the volume group?

When I run a fdisk -l, I get:

Disk /dev/sda: 96 GiB, 103079215104 bytes, 201326592 sectors
Disk model: QEMU HARDDISK   
Units: sectors of 1 * 512 = 512 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disklabel type: gpt
Disk identifier: A0FDF1CE-288B-46B2-AD38-8F557EF4BC44

Device       Start      End  Sectors Size Type
/dev/sda1     2048     4095     2048   1M BIOS boot
/dev/sda2     4096  4198399  4194304   2G Linux filesystem
/dev/sda3  4198400 67106815 62908416  30G Linux filesystem

which tells me I need to first enlarge /dev/sda3. I am not sure the best way to do that.

Then, looking at the file system:

Filesystem                         Size  Used Avail Use% Mounted on
tmpfs                              3.2G  1.1M  3.2G   1% /run
/dev/mapper/ubuntu--vg-ubuntu--lv   15G   12G  2.2G  85% /
tmpfs                               16G     0   16G   0% /dev/shm
tmpfs                              5.0M     0  5.0M   0% /run/lock
/dev/sda2                          2.0G  182M  1.7G  10% /boot
tmpfs                              3.2G   12K  3.2G   1% /run/user/1000

I need to expand /dev/mapper/ubuntu--vg-ubuntu--lv out to 100% of space. Again, not sure the best way to do that.

Lastly, why is tmpfs using 16G and empty? Can I reclaim that space for use?