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Props rajinsharwar, ayazahmed12.

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Test this pull request with WordPress Playground.

1. Added validations and _doing_it_wrong fro the arguments passed.
2. Added a new filter that can be used to change the Tooltip icon image. This is similar to the one we have in add_menu() function. We can now pass the URL, or the SVG, or the dashicon class, or even the "none" to style using CSS.

Example usage:

add_filter( 'wp_tooltip_icon', 'my_filter', 10, 2 );

function my_filter( $icon_url, $field_id ) {
    $icon_url = "data:image/svg+xml;base64,PHN2ZyB3aWR0aD0iMjAiIGhlaWdodD0iMjAiIHZpZXdib3g9IjAgMCAyMCAyMCIgeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzIwMDAvc3ZnIj48cGF0aCBmaWxsPSIjYTdhYWFkIiBkPSJNMTcuNiA4LjVoLTcuNXYzaDQuNGMtLjQgMi4xLTIuMyAzLjUtNC40IDMuNC0yLjYtLjEtNC42LTIuMS00LjctNC43LS4xLTIuNyAyLTUgNC43LTUuMSAxLjEgMCAyLjIuNCAzLjEgMS4ybDIuMy0yLjJDMTQuMSAyLjcgMTIuMSAyIDEwLjIgMmMtNC40IDAtOCAzLjYtOCA4czMuNiA4IDggOGM0LjYgMCA3LjctMy4yIDcuNy03LjgtLjEtLjYtLjEtMS4xLS4zLTEuN3oiIGZpbGxydWxlPSJldmVub2RkIiBjbGlwcnVsZT0iZXZlbm9kZCI+PC9wYXRoPjwvc3ZnPg==";

    return $icon_url;
}

This will show an SVG now in the tooltip.

Example:

3. Added a new action hook that's fired just before the tooltip is rendered in HTML.
4. Loading the styles and scripts for the tooltip before it's rendered to not show a slightly broken tooltip.

Screenshots:

Using Tab navigation: