Your "old" one is likely 1.5mmAccording to this table 1.0mm^2 mains cable should be able to carry 10A safely. I have been using a 20m extension cable on my 1800W mower that has an external diameter of 7mm and it has worked reliably for many years - I am not sure what type of wire is inside but I would guess that it is only 1.0mm^2.
The problem with cheap extension cables is usually the connectors. If the 15A plug socket does not make good contact with the prongs of the plug it will get very hot and fail after a short time. Some of the Chinese electrical equipment that I have purchased from local hardware stores is of a very low quality but some products have exceeded my expectations. That extension cable also has a good selection of different plug types.
I've only seen 1mm cable sold on rolls fairly recently. Similar to how the rolls used to be metal, and are now plastic crap. New 1mm is also possibly stranded copper, which will rate for less than solid core.
Cheap currency = cheap crap sold here.
I wonder if that even has SABS approval (the 1mm 20m roll)
The lawnmower cable you link to may claim to be 2500w capable, but thats just a claim.
If I was getting an extension cable - I'd get something like this - https://www.adendorff.co.za/product/kosmo-reel-30m-extension-cord-with-reel-1-5-mm/
Sure, its double the price, but its also built to last.