Can you provide screenshots of the Dashboard > Updates page and the Tools > Beta Tester page?
Here’s my Beta Tester page:

After saving, this is what I see in Dashboard > Updates (I’m currently at WP 5.7.2):

After clicking “Update now”, it says I’m in version 5.7.2 still. And if I head back to Dashboard > Updates, I see:

Clicking “check again” doesn’t do anything.
Clicking on the button that’s labelled “Re-install version –en_US” just shows a blank gray admin screen
Can you install and activate https://ww.wp.xz.cn/plugins/updates-api-inspector/
From Tools > Updates API Inspector select the Core tab.
Can you then copy/paste the Request and API Response?
Here you go, this is after I’ve gone through and clicked the “Update now” button:
array(
'timeout' => 3,
'user-agent' => 'WordPress/5.7.1; http://wpbeta.local/',
'headers' => array(
'wp_install' => 'http://wpbeta.local/',
'wp_blog' => 'http://wpbeta.local/',
),
'body' => array(
'translations' => array(),
),
'query_string' => array(
'version' => '5.8-alpha',
'php' => '5.6.39',
'locale' => 'en_US',
'mysql' => '8.0.16',
'local_package' => '',
'blogs' => '1',
'users' => '1',
'multisite_enabled' => '0',
'initial_db_version' => '47018',
'channel' => 'beta',
),
)
Can you also paste the API Response?
Sorry, wasn’t able to get back to this. I’m not certain now whether it was the RC release or what, but it now works, was able to update to 5.8-RC2 using the same steps.
Marking this as resolved for now until someone else encounters this for the next update.