How to place facet block in views page header? (not regions)
Firstly, I would recommend that you consider placing the facet block right above the view instead of performing a surgery on views :D

That said, here's what I think might work:

Solution 1: Views Header


Views allows you to attach rendered blocks in the views header.
In the views UI, click the Add button in the Header configuration.
Then choose Rendered Entity - Block and choose the facets block you want to display


Solution 2: Attachment Before


Write a hook_views_post_build()
In this hook, render the facet block as the attachment_before of the view.


See this answer about rendering blocks programmatically

You might face some difficulties with views caching, etc, but you can fine-tune the views build to alter the caching rules.
If you don't like the idea of Attachment Before, you can also consider adding a header item with a custom token like @facet:foo@ and then replace this custom token with a rendered facet block in hook_views_pre_render()


I hope this helps!