A tire’s rolling resistance is about 90% controlled by the tread compound - the kind of tread rubber and how much is used. The type of tire - All Season, All Terrain, Highway, etc - does NOT have much effect - except to say that some types of tires use more tread rubber (ala All Terrain and Winter).
In order to get a low RR, either the treadwear or the traction has to be sacrificed (sometimes both!). The tires that get the lowest rolling resistance are the OE tires - the tires that come on new cars - and that’s why OE tires have such a bad reputation. It isn’t because they are cheap (they are NOT inexpensive, nor made using short cuts), it’s because the tread compound is designed to meet the car manufacturers requirements, which emphasizes low RR, and not wear.
However, there are some tires designated with “LRR” - Low Rolling Resistance - but that is a relative term. It means better fuel economy compared to tires with similar wear and traction characteristics. In some respects, the term is misleading because tires with truly low RR WILL sacrifice treadwear and/or traction - and it is possible to have a tire with lower RR than a tire with a LRR label.
If the gang wants, I can explain why the government has not yet demanded that a tire’s RR be designated in some way, like they have for traction, and treadwear.