It may be even tighter than you think since the "Available" storage value is very misleading, but for some reason Apple decided to display this value every where. You need to look at the actual Free space value shown in Disk Utility. You should always have at least 20GB+ of Free storage space at all times for the normal operation of macOS.....you may need to have even more depending on the workloads since that 20GB disappears very quickly.
If you completely run out of Free space on an APFS volume, then you may not even be able to delete anything to make more room due to how the APFS file system works & how Apple has implemented it.
You can use OmniDiskSweeper to locate the largest files & folders, but even this type of app is unable to see some areas of the drive (even within your own home user folder) due to all the recent privacy & security features, but it should allow you to see stuff that you should be able to delete within your home user folder(s).
With an APFS volume the data you have deleted may still reside in hidden APFS backup snapshots for some time until the backup app automatically deletes the snapshots.
View APFS snapshots in Disk Utility on Mac - Apple Support
I hope you have frequent & regular backups since there are a lot more new ways to lose access to data stored on the internal SSD of the recent Macs due to all the hardware, software, and security changes. Completely running out of Free storage space is one of those things.