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I don't have this option on tweetdeck, only a add to collections, gives me a popup with no content. Nice.

It’s on the official site, I’m not sure of 3rd party app support. To view your bookmarks, https://mobile.twitter.com/i/bookmarks

I only see it on the mobile site.

It's found to the right of the heart button.

tweetdeck is technically first party, twitter acquired the team many many years ago