Depending on the current version of macOS on this Mac, it may require having at least 50GB of Free storage space. You neglected to give us relevant details on your current version of macOS and also how much Free space Disk Utility is reporting.....ignore the "Available" storage value shown everywhere in macOS since it is very misleading and is not synonymous with Free. The Free storage space value is the only & most critical storage value there is.
It is also important to know the size of the physical SSD in your Mac since a 120GB SSD can just barely run macOS & store a very small amount of data since you should always at minimum have at least 20GB+ of Free storage space at all times....even that 20GB can disappear very quickly even with light use. Ideally you should have at least 50-100GB of Free space.....of course 100GB of Free space is impossible on a 120GB SSD. Bad things happen when macOS runs out of storage space including not being able to delete any data due to how the APFS file system works.
Plus when you delete files, it may take 24-48 hours after Time Machine (or some third party backup software) transfers the backups to external media before you see the Free space actually appear ready for use (you will see the "Available" space increase, but you won't have access to it right away).
