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The same H1 tag content in header OR use page specific H1? [closed]

We have a WordPress website which has the site title in the header.
The site title in the header has the H1 tag.
The result is that on every page the H1 tag appears as the first heading and has the same content.

The alternative is that we make the content of the H1 tag relevant for each page.
In this case we will change the site title in the header into H2.
Doing so, the first heading on each page is no longer H1.

Does anyone have an idea on what is best practice in terms of SEO?

OR