Classic Teams users can download their saved messages and files to a local folder that they can open in new Teams.
Mark a message as saved in Microsoft Teams - Microsoft Support
So, you mean that the links in the excel file will still take me to the specific saved message. This is good to know.
However, the bigger question is: if Save Messages is disappearing, what can I use in New Teams to replace the functionality I am losing?
Use Case: I'm in the middle of a task and a Teams message comes in. I briefly look at the new message and see that it will require an action on my part. To make sure I don't forget about it, I save the message and return to my original task. Later, when I have time, I check my saved messages and take action or add it to the appropriate workflow/backlog as necessary.
If there's a convenient alternative in New Teams for this use case, I'm willing to listen.