I'm moving my comment here because I'm not sure why people are repeating the false information about 3rd parties have lower price than direct booking because of some contracts.

That's simply not true. I just did a search now to see if anything has changed. I randomly searched for hotels in the Seattle area for a 5/18 reservation. The 3rd item in a hotel's result [1] is the hotel's direct booking price. It matches the same reservation on the hotel's website [2]. Another hotel's result [3] has the lowest price as direct booking. Again for another hotel in NYC [4], the 3rd item is the hotel's direct price.

[1] https://i.imgur.com/XtDkLZj.png

[2] https://i.imgur.com/gHJgB3I.png

[3] https://i.imgur.com/MVVqmFG.png

[4] https://i.imgur.com/WAIuM16.png