Can I use wp_oembed_get to detect a valid embeddable link or is there a better way to do so?

The regex patterns for matching embeddable URLs are stored in WP_oEmbed, which has the method get_provider() for checking if a given URL is an embeddable URL for a supported provider. Just set the discover argument to false if you don’t want to actually send a request to the URL to test it, and just want to match the regex:

$url="https://twitter.com/WordPress/status/1169427892406644736";
$oembed   = new WP_oEmbed();
$provider = $oembed->get_provider( $url, [ 'discover' => false ] );

if ( false !== $provider ) {
    // Is embeddable.
}