Both the jar itself and the lid were printed in Spiral Vase Mode. This model was designed to be printed with a 0.4mm nozzle.

Completed Jar Dimensions:
If your tolerances are correct, the lid should stay snug and tight, and it should hopefully keep its contents in even if flipped upside down. I was even able to get a print to hold in some water upside down! (see the photos taken at the kitchen sink).
I have added a “TEST_Pleated_Jar_Spiral_VaseMode.stl” file to test your tolerances. Print out a Jar Lid in vase mode and this test file to see if the threading matches and screws tightly together. The lid is the same for both the short and tall jar.
This print was made on a stock Prusa i3 MK3S+ using the stock 0.4mm nozzle with 0.2mm layer height with all generic ABS settings on PrusaSlicer using the Spiral Vase Mode. I am interested in seeing how prints using a larger nozzle will turn out and how much tweaking will be required, so please post photos and your adjustments if you are successful!
If you are planning to use this for long term, I would suggest printing in PETG or ABS or some other heat resistant filament to prevent warping over time (I've had PLA vases warp during some hot days during the summer).
Models in Photos
The models in the photos were all made using ABS filament. The light blue plastic is from Hatchbox, and the clear filament is from Octave (found on Amazon).
The model in the photos were printed using the following materials/settings:
I am a 3D modeler, and this is my original creation! Please comment with your results and photos!
Edit (Oct 6, 2022): Added a tall version of the jar to complete the Kimchi jar set.
The author hasn't provided the model origin yet.