does fuel efficiency matter on tyre's ?

The Eagle F1 is C fuel A grip
https://www.tyreleader.co.uk/car-tyres/goodyear/eagle-f1-asymmetric-3/255-35-r19-96y-750569
Pilot sport 4 also C and A
https://www.tyreleader.co.uk/car-tyres/michelin/pilot-sport-4/255-35-zr19-96y-751500

Don't get hung up on fuel economy, the difference between an A and a G rated tyre is around 7.5% . So roughly just over 1% difference per step.
Two steps difference is 2.5%.
Wide low profile performance tyres like a 255/35/19 struggle to get low ratings. Cheap tyres have a lot less grip especially in wet and cold conditions despite maybe having a B rating.
Different versions of the same tyre can have different ratings dependent on what the tyre is specified as.
A Mercedes OE tyre F B
https://www.tyreleader.co.uk/car-tyres/continental/conti-sport-contact-5p/255-35-zr19-96y-526833
An Audi OE tyre F A
https://www.tyreleader.co.uk/car-tyres/continental/conti-sport-contact-5p/255-35-r19-96y-735400