Being able to embed YouTube and Twitter is very convenient, but I feel that the variety of embed blocks has become so large that it can be difficult to find what you’re looking for.

I think it would be okay to hide things that are particularly unfamiliar from the inserter.
How to hide it
In conclusion, you just need to set the scope of the target variation to block only. For example, if you want to hide YouTube and Twitter, you can write the following code to hide them.
/**
* WordPress dependencies
*/
import { getBlockVariations } from '@wordpress/blocks';
import domReady from '@wordpress/dom-ready';
domReady( () => {
const registerEmbedBlocks = [
'youtube',
'twitter',
];
getBlockVariations( 'core/embed' )?.forEach( ( block ) => {
if ( registerEmbedBlocks.includes( block.name ) ) {
block.scope = [ 'block' ];
}
} );
} );
This is inspired by the fact that in the core source, deprecated variations were hidden from the inserter by fixing their scope to a block.

Will unregisterBlockVariation not work?
You can also use unregisterBlockVariation
, but this is done because it removes the registration of the variation itself, so the title and icon will no longer be displayed.

unregisterBlockVariation( 'core/embed', 'youtube' );
ちなみにWordPressテーマMoneでは以下のバリエーションは非表示にしています。
By the way, the following variations are hidden in the WordPress theme Mone.
/**
* WordPress dependencies
*/
import { getBlockVariations } from '@wordpress/blocks';
import domReady from '@wordpress/dom-ready';
domReady( () => {
const registerEmbedBlocks = [
'flickr',
'cloudup',
'imgur',
'kickstarter',
'reddit',
'issuu',
'mixcloud',
'scribd',
'smugmug',
'crowdsignal',
'reverbnation',
'reverbnation',
'pocket-casts',
'animoto',
'screencast',
'ted',
'videopress',
'bluesky',
'wolfram-cloud',
'wordpress-tv',
'tumblr',
];
getBlockVariations( 'core/embed' )?.forEach( ( block ) => {
if ( registerEmbedBlocks.includes( block.name ) ) {
block.scope = [ 'block' ];
}
} );
} );
However, as you can use it normally as shown above, just place a simple embed block and enter the URL you want to embed!