How to investigate delay from hibernate to shutdown?

Cache/Buffer will never be dropped to a swap disk/file. It will be freed up, when more RAM gets allocated.

Well, you have 32GB RAM and 16GB SWAP. After time, you will not be able to hibernate, since there have to be written a full image. If Linux decides to drop RAM pages to the SWAP, then this will add up to the image.

32GB + swapped space (e.g. 2GB) = 34GB. You would at least theoretically need 36GB of swap space, since it writes an entire image of the 34GB, not just 32GB, because the swapped 2GB count as “inactive” RAM. You can drop cache plus deactivate and activate swap to mitigate the problem, but more swap space would be the easy solution.

Since you can possibly have a lot of RAM usage, 64GB swap would be very well-equipped. But at least 1.5x32GB = 48GB, if Hibernation is really what you need.

I would recommend reading this to improve the swap problem: