I have no problems with synthetic oils, only synthetic oil users who have had one too many glasses of the synthetic oils will fix every problem cool aid.
You should use the oil that a product was designed to run.
As the properties of synthetics do vary from those of a standard oil substitiuting one for the other can cause a loss in performance, particularly in hydros .
Prime example is wet clutches where most will not grip properly if exposed to a synthetic oil
And the use of the word "synthetic" itself
There are just a handful of truely synthetic oils on the market that were developed for use in conditions that a mower will never see, mainly F1 race engines & fighter jets .
People seem to think that "synthetic oils " are some sort of magic product where as they are really just Dissassembled then RECOMBINED , a process that we have in fact been doing to a lesser degree from the day we first used oil .
As for mower engines, apart from a couple of EFI engines using synthetic will do nothing but cost you more and do more enviromental damage.
A mower engine is the cheapest nastiest lowest cost shortest life engine it is possible to make so filling it with "magic goop" is a waste.
So the long & short is
If it was designed to run with synthetic oil then use synthetic oil
If it was designed to run standard oil use standard oil
Pretty simple as far as I can see.