Freeing up space · Free Up Space wizard and button
When does the Manage snapshots suggestion appear after Free Up Space?
Short answer: It appears in the Want more space? panel when five or more local snapshots are holding deleted space. It opens the Local Snapshots manager; you can also open that from More → Local Snapshots.
It shows up in the Want more space? panel when there are at least five of macOS's local snapshots holding on to deleted space. Tapping it opens the Local Snapshots manager, where you can see which snapshots are already on your Time Machine backup and release the space they're holding.
If the chip isn't there, your Mac isn't holding enough snapshots for them to be the likely cause. You can still open the manager any time from More → Local Snapshots….