I can't resize my root partition

You can't work on partitions that are currently mounted.

Make sure that you have a good backup of your important Ubuntu files, as this procedure can corrupt or lose data.

Keep these things in mind:

• always start the entire procedure with issuing a swapoff on any mounted swap partitions, and end the entire procedure with issuing a swapon on that same swap partition

• a move is done by pointing the mouse pointer at the center of a partition and dragging it left/right with the hand cursor

• a resize is done by dragging the left/right side of a partition to the left/right with the directional arrow cursor

• if any partition can't be moved/resized graphically, you may have to manually enter the specific required numeric data (don't do this unless I instruct you to)

• you begin any move/resize by right-clicking on the partition in the lower pane of the main window, and selecting the desired action from the popup menu, then finishing that action in the new move/resize window

Do the following...

Note: if the procedure doesn't work exactly as I outline, STOP immediately and DO NOT continue.

• boot to a Ubuntu Live DVD/USB, in “Try Ubuntu” mode
• start gparted
• move the entire nvme0n1p9 partition all the way to the right
• resize the right side of nvme0n1p8 all the way to the right
• click the Apply icon

Use "Partition | Resize/Move" menu option to move the home partition to the unused space then resize the root partition to the adjacent unused space. Search online for "gparted move partition to the right" to get details if needed.