How important is it to use manufacturer brand fluids

TRW makes OEM parts. They are different. They sell product to the manufacturers under contract and supply the aftermarket. Not all aftermarket parts makers are like this.

There are many parts makers and rebuilders out there that don’t have that relationship with manufacturers. They make the parts to spec, but use their own QC or use an outside QC to check them. Some are good, others are crap. Reputation is king with the good ones.