How to get string from add_theme_support(‘title-tag’) for meta tag and beautify?

I don’t have a good way to query a title string to fill in the content

You can use wp_get_document_title() to get the document title.

So for example in your case: (see the docs for details on esc_attr())

<?php
// Put the title (string) in a variable.
$title_esc = esc_attr( wp_get_document_title() );
?>
<meta property='og:title' content="<?php echo $title_esc; ?>"/>
<meta property='twitter:title' content="<?php echo $title_esc; ?>"/>

I want to customize title format, like setting blog’s name position

You can do that via the document_title_parts hook.

But first, the document title has the following parts by default, and they’re passed as an array to callbacks hooked to document_title_parts:

| Part                                | Array key | Optional | Position |
|-------------------------------------|-----------|----------|----------|
| Title of the viewed page.           | title     | No       | 1        |
| Page number if paginated.           | page      | Yes      | 2        |
| Site description when on home page. | tagline   | Yes      | 3        |
| Site title when not on home page.   | site      | Yes      | 4        |

The “optional” state means that the array item may or may not exist on certain pages — e.g. on page 1 of a category archive, the page item doesn’t exist (or is excluded) by default, but on page 2 and above, page is included.

So for example, if you want the blog/site title to be the first instead of the default last:

function my_document_title_parts( $title ) {
    if ( isset( $title['site'] ) ) {
        $site = $title['site'];  // get
        unset( $title['site'] ); // unset
        // Then put it at the top.
        $title = array_merge( [ 'site' => $site ], $title );
    }
    // Remember to return an array.
    return $title;
}
add_filter( 'document_title_parts', 'my_document_title_parts' );

And based on the above code, here are some sample output of var_dump( $title ):

// Home page.
array (
  'title' => 'My Site',
  'tagline' => 'Just another cool WordPress site',
)

// Category page 2.
array (
  'title' => 'Uncategorized',
  'page' => 'Page 2',
  'site' => 'My Site',
)

// Single Post.
array (
  'title' => 'Markup: HTML Tags and Formatting',
  'site' => 'My Site',
)

or using a different separator

You can do that via the document_title_separator hook.

Here’s an example for using | than the default - (i.e. a hypen):

function my_document_title_separator( $sep ) {
    return '|';
}
add_filter( 'document_title_separator', 'my_document_title_separator' );

Notes

• Changing the title parts via document_title_parts or the title separator via document_title_separator will also change the title parts/separator which WordPress use in the title tag. There are solutions such as using a closure, but I’m not giving any examples for that (for now).