That ‘rule of thumb’ is wrong for Microsoft and is wrong for Linux. Something like it used to be suggested in the late eighties or early nineties, when relatively few megabytes of ram was the norm; even then, for the ‘rule’ to have any utility, computers that had heavier workloads had to to have more ram, which may have sometimes been the case, with the then cost of ram, but was not universally the case.
I recently went from 2GB of memory to 8GB. However I noticed that my swap size is only a little over 2GB.
For normal operation, if the workload has not changed, this means that you need less swap; as lOtz1009 has pointed out, if you suspend to disk, you may need more. OTOH, you might have bought more ram because the workload (or, potentially, bloat in some application(s) that you use) has increased…
(Whether or not you suspend to disk) I would not reduce the amount of swap, unless you are really very pushed for disk space; the normal case is that wastes a little disk space, of which you have plenty - not a problem.
If you do have to add swap space for suspend to disk to work reliably, add another swap partition. It can be easy (depending on how your partition table looks currently and where you have spare space), and it works.
If so, how do I adjust it to the correct size? And is there a way for the system to just automatically calculate the correct size?
Prior to 11.2 (?), SUSE did not compress on suspend. In those days, you needed an amount of swap equal to the maximum memory consumption (ram+ swap) that you use. This is easy to measure from ksysguard (or similar).
Currently, you should need less, but as I don’t know how to quantify how much less, I’d still go for the same amount, maybe just a shade less, if that came to a convenient round number, or was the amount that you have now.