2020 Silverado 1500 6.2L towing

[Cuemark8]

I too am confused about Phillips 66 oil that's made by Castrol.

I don't understand where there is any confusion. Outside of the United States where they don't brand Motorcraft products Ford works extensively with Castrol to supply their motor oils.
I know that Ford specifically worked with Castrol developing an oil for the European spec 1.0Ll EcoBoost engine.
Ford even created a new spec. It was a WSS 948 spec
Also since Ford does not brand a Motorcraft oil in other countries the premium oil that they sell at the dealerships is Castrol Magnetek and when you buy a jug of it it even has the Ford logo right on a jug of oil.
I also know that the Shelby Mustang comes factory fill with Castrol Edge oil and so does the Ford GT.
I am aware that Motorcraft oil is made by Phillips 66.

 

[Cuemark8]

Was not here to argue Ford oils. The OP asks for a quality oil.
I'm a fan of the Castrol Edge. Proven, works well. I think Castrol Edge and Mobil1 are 2 best mainstream oils on the market.
OP has issues with oil consumption. In spec grade of 0W-20 the Castrol Edge was an ever so slightly more viscous .

Kinetic viscosity at 100C is 8.6 for Mobil 1 EP.
Kinetic viscosity at 100C for Edge EP is 8.7.
That's OW-20 grade.