I empty trash and available space goes DOWN?

macOS 10.13+ uses the new APFS file system where an APFS snapshot will retain deleted data until the APFS snapshot is deleted. Usually these snapshots are deleted automatically after about a week or after all your backups have been completely transferred to your external backup drive(s). macOS creates APFS snapshots when updating/upgrading the OS.

If you need the space immediately make sure all your backups are completely transferred to your external media. Then if you still don't have room, then you can use the information in this article to thin or delete APFS snapshots:

https://derflounder.wordpress.com/2018/04/07/reclaiming-drive-space-by-thinning-apple-file-system-snapshot-backups/