This one is an old furfy.
I also do a bit on a lawn contractors forum, and there is the anecdotal theory that 98 premium will make the mowers go harder too. (rubbish)
The only reason to have a high octane fuel is to cope with higher compression ratios.
If you have a compression ratio of 10:1 or higher, igniting the fuel the same BTDC as a 8:1 engine will burn the fuel faster and increase cylinder pressure enough to make the charge detonate (pinging). TO avoid pinging the timing has to be retarded in high compression engines that are trying to run standard unleaded fuel.
If you have a compression ratio of 8.5:1 (tb42), running 98 premium means the fuel will burn slower - effectively retarding the timing and making the engine run hotter with less efficiency. Modern engines that set ignition timing based on knock sensors will run almost identical to running the engine on 91 unleaded. However the ignition timing will spark further before TDC which can rob an engine of power.
If you really want to test the theory, run your engine on LPG - it has an octane equivalent of 110. = Runs hot with less power.
Increase the compression to around 11:1 and run LPG = better fuel economy, more power and cooler running.
Run 11:1 compression with wet injection LPG and you'll get better power and fuel consumption than the same engine fuelled with petrol.
May as well try feed a bulldog rib eye fillet steak to make it run like a greyhound.