Teams periodically forces me to "upgrade" to the New Teams. If this happens to you, do not worry! Your bookmarks are still there. All you have to do is toggle back to Classic Teams and your bookmarks will be waiting for you.
Dear Microsoft, can you stop forcing us to upgrade to New Teams? It is frustrating.
All, please be aware, that at least for Office 365 customers, Microsoft plans on forcing an upgrade to the New Teams at the end of March 2024. If you have not adopted the new teams by then ( and by that I mean come up with some sort of work-around for not being able to save messages) you will get moved to the new teams and you will not have access to those "Saved Messages"
Microsoft promises that a "similar feature will be available later this year {2023} now reads "... in the future. MS also recommends that you should download your saved messages and file to a local directory before you switch to the New Teams and that can be opened in teams, but that won't help your ability to use that "Saved Messages" feature in the future. As of this writing on January 3rd, 2024, I have not seen anything that suggests a new feature is available or even becoming available.
Just be warned, New Teams is coming to a computer near you by the end of the 1st quarter of 2024.