Your Mac reports 54.77 GB of available storage, of which 54.15 GB is identified as purgeable.
According to Apple, available storage includes both free storage and purgeable storage.
Purgeable space is storage that macOS can reclaim when additional space is needed.
Apple explains that available space can include purgeable space that macOS can free automatically by removing data such as certain caches or other items it has identified as removable.
You cannot manually delete the items designated as purgeable through Apple's supported storage-management tools; macOS manages that process itself. (Apple Support)
It is therefore important not to interpret the 54.15 GB of purgeable storage as 54.15 GB of files that you need to locate and delete.
Purgeable storage is a category managed by macOS, and the amount reported can change as the system determines how much space is needed.
If you want to deliberately increase the amount of free storage on the Mac, you should instead remove data that you no longer need. This can include large personal files, downloads, applications, media, backups, or other data.
You can also move large files or libraries to an external drive if you want to keep them without storing them on the Mac.
When you delete files, the storage they occupy is not released until you empty the Trash. Once the Trash is emptied, that space becomes available as free storage. Deleting a file does not simply convert the file's storage into purgeable storage; it releases the space as free storage. (Apple Support)
Apple provides tools for identifying files and other data that are taking up storage, along with instructions for deleting items you no longer need. (Apple Support)
If the reason for investigating the storage is that a macOS update is reporting insufficient space, Apple specifically recommends starting the Mac in Safe Mode in some circumstances.
Safe Mode clears certain system caches, which can temporarily make additional storage available. These caches can be recreated by macOS as needed, so Safe Mode should be regarded as a troubleshooting measure rather than a way to permanently eliminate purgeable storage. (Apple Support)
If the update continues to fail, Apple also recommends additional troubleshooting steps depending on the error, including checking the Internet connection, attempting the installation from macOS Recovery, and using Disk Utility from Recovery to check or repair the startup disk. (Apple Support)
In summary: the 54.15 GB of purgeable storage does not need to be manually purged. macOS is responsible for managing that space and reclaiming it when necessary. If you need to create additional free space yourself, delete or move data you no longer need and empty the Trash.
If the issue is specifically an inability to install a macOS update despite having substantial purgeable space, Safe Mode and Apple's other recommended installation troubleshooting steps are the appropriate next measures.