After plugging in my external HDD to my MBP Pro, it always takes about 5-10 minutes for my Mac to recognize it. When I first did a Time Machine Backup with this same HDD several months ago, my Mac recognized the HDD within a few seconds. It's a 4 TB HDD with 3.18 TB available. It's an APFS Volume.
MacBook Pro 16″, macOS 10.15
Have you been experiencing any problems with the HDD? If the drive is several years old it may need replacing. We replace ours at 5 year intervals.
Open Disk Utility and run First Aid on the drive.
You can always erase the drive and start over. On a properly operrating Mac the short period you don't have a full backup is a very small risk.
Have you tried other ports and cables?
Have you installed and run any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your Mac?
Time Machine Backups - Why does it take so long for my Mac to recognize my WD Elements 4 TB external hard drive disk?
