1. Now behind that popup window, where the main window is for GParted, see if /dev/sdc2 has that little icon at left that shows it is mounted (it would appear so from the text above, at Status.
2. If so, you can right-click that line and choose unmount. Do so. It will take a moment.
At the top left of the pane, you should have a toolbar with icons, numbering 6 or 7, and you can run your mouse cursor over them and see Smart Tips that explain the functions.
3. You can either click the line that shows /dev/sdc2 and it will highlight, then go to the icon that says Delete and click it, or else without highlighting, just right-click the line and choose delete. You will form a preference over time - 2 or 3 ways to do the same thing, same as Windows.
If you choose the latter method, it will show the operation pending at bottom of window, and go to the icon at top that says Apply All Operations and click.
The partition will be deleted and the space returned to Unallocated Space.
You can now choose to create a new /dev/sdc2, for Timeshift snapshots storage.
4. Right click in the Unallocated Space, and choose New, a popup window will appear. If you want 200 GB again -
5. Leave Space Before as zero, tab to the next field down and type in 204800 and press tab, the bottom field will be calculate as Unallocated Space remaining.
Leave it set to MiB, not cylinders, they are a relic from the past.
6. Right-hand side, leave the Partition as Primary, and the file type may be showing as EXT4, all and good. If it is showing as BTRFS, click beside it and change to EXT4. OK the changes, the operation pending will appear at bottom, and click the check mark icon at top to Apply All Operations.
If all of the above works,
7. You will have a new /dev/sdc2 - right-click it and choose Label, not Name. You'll get 11 to 16 characters to write a descriptive title, I just use Timeshift, or since I have 3 drives, Timeshift-WD for my Western Digital external drive. Operation pending will appear and OK the Apply Pending Operations.
We can then look at Timeshift and make adjustments to reflect the new regime.
Report back with any questions or outcomes.