At this point, nobody should trust anything shared from Twitter to keep working. If you embed tweets in your blog, newspaper, whatever, you need to start saving the embedded content locally. (Or just, *sigh* screenshot it.)
https://www.theverge.com/2023/4/6/23673043/twitter-substack-embeds-bots-tools-api
If they’re already blocking embeds from one site, it’s only a matter of time before they start blocking them elsewhere. Like, say, in newspapers with unfavorable coverage. Or they make embeds paid-only content.