A tweet from Aiden Moher: Twitter uses a service to capture analytics data for outbound links (using the https://t.co domain), and that service lost API access (presumably due to the new system that charges companies API access), so now outbound links aren't working. This is presumably also why images aren't working.
https://files.mastodon.social/media_attachments/files/109/977/516/007/744/932/original/bb873df5fefe98ab.png