When trying to verify a site in Search Console using the Google Tag Manager method, Site Kit's Tag Manager container snippet fails and is flagged as being in the wrong location on the page:

Related support topic: https://wordpress.org/support/topic/gsc-says-google-tag-manager-snippet-is-in-the-wrong-location/
The documentation has code placement requirements for this verification method. Testing an alternate method to insert the container (i.e. plugin) provided successful verification.
See also #721
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Tag_Manager::register for invoking print_gtm_no_js on the wp_body_open actionwp_body_open function and its corresponding action were only introduced in WP 5.2 so we need to keep the existing action as well.did_gtm_no_js property to Tag_Managerprint_gtm_no_js if did_gtm_no_js is setdid_gtm_no_js in print_gtm_no_js when invoked the first timebody tag as commonly expected.IB ✅
We should also use a very early priority on wp_body_open - there's no guarantee we're the earliest, but let's do our best. WordPress is terrible with this anyway, I'm perfectly fine with using something like -9999 :)
Tested the fix with @ernee
Installed SK 1.7.1 zip, activated and connected Tag Manager and inserted Site Kit's container snippet on hellogoodbye.today
Setup a non verified secondary google account and verified from the Search Console account using the Google Tag Manager.
Notice:

Passed QA ✅
Most helpful comment
Tested the fix with @ernee
Installed SK 1.7.1 zip, activated and connected Tag Manager and inserted Site Kit's container snippet on hellogoodbye.today
Setup a non verified secondary google account and verified from the Search Console account using the Google Tag Manager.
Notice:

Passed QA ✅