I would upgrade the fluid. I also wouldn't worry about the "marketing" from the brand. Its not for the consumer to understand the marketing. Marketing is to make the sale. All you have to do is match the specifications. I believe that you were confused concerning 'clutch' friction/traction modifier vs silly nano-marketing additive to reduce frictional wear with at the pump/gears/bearings.....
My recommendation is to understand the adjustments within your transmission and adjust as needed also.
Type F would varnish up pretty quickly and you'd see typical seal wear, component scuffing, governor sticking... I would not say that any of the new conventional type-F's are any better than what was available in the 1970's. Back then, simple 2 and 3 speed transmissions had rebuild kits that cost $20. Typically, and for too many, the 1st fluid change occurs when the shop rebuilds its. I could pull, rebuild, reinstall one in a couple hours. So, adjust it and maintain the ATF, as needed for your driving style, mods, and power level.
When it comes to ANY transmission, upgrade when possible. The synthetic or blend fluids are an easy upgrade path, especially when the transmission is outside of its original parameters or expectations(higher HP motor, shift kits.....). I would not use any common typeF from the autopart store. Upgrade the ATF and keep the transmission clean. Or, get familiar with the rebuild manual.
Concerning the ATF cooler, depending on vehicle, most will toss in whatever fits. If you want to pick an appropriate cooler, you install an ATF temperature gauge, get the temps, and see if its needed for the daily drive or illegal redlight races. Some inline "PH8A" filter kits come with spots for temp sensors/senders. Otherwise, you drill the pan for one and mount up a gauge. Since OE filtration is a joke, consider the remote filter kit and get that temp gauge too.
If average ATF temperature is acceptable, but once in a while gets a little too warm, then sometimes all you need is a deep sump and matching dump sump 'pickup' filter, and maybe skip the add-on ATF cooler. Some go too big with add-on ATF coolers and conventional Type-F is not known for is cold performance.