Recently, I have run into this issue recently, and thus I have built myself a configurable Custom Lightning Header (https://github.com/xdf29/XD_Custom_Lightning_Header_Project) (with LWC) for Lightning App Page. You may get it here. Hope this is helpful.
Can you try checking the below link that seems to having same requirement to implement.
>> https://salesforce.stackexchange.com/questions/260858/hide-standard-page-header-in-custom-lightning-app-page
I hope this helps and in case if this comes handy can you please choose this as best answer so that it can be useful for others in the future.
Regards,
Anutej
It's not possible.
An Idea is already raised for it. Based on the Votes it will be implemented in the future by product team.
Idea Link:
https://trailblazer.salesforce.com/ideaView?id=0873A000000TusWQAS
I hope you find the above information is helpful. If it does, please mark as Best Answer to help others too.
Regards,
Salesforce Support.