How can I recover photos from an external hard drive?

When you wrote "The drive will not open", do you mean that the system cannot mount the volume?

Try use a different cable or different port or a different computer. Some of my older external drives could not be mounted only Mac with Sequoia, but I could still use them on my older Macs with macOS 10.14 Mojave.

if you manage to open the old external drive, use the opportunity to run disk utility and check the drive, then save the data to a new drive.

If the drive does not become visible in the Finder, it looks like there is an issue with the drive itself.

First there are some simple steps. Try another cable. Do a restart of your computer. Try another Mac. Inspect with disk utility.

If it is a Photos library you cannot open, you can go to the Finder, select the photos lib, do a control click and select 'show package contents'. This way you can enter the library and hopefully find all your photos back.

Have you tried the Disk Utility and its First Aide routine?

What format is the external drive? Check it via Finder > Get Info. Should be APFS or MacOS Extended, other formats are not supported for Photos libraries and might cause other issues as well.

As léonie asked,

"When you wrote "The drive will not open", do you mean that the system cannot mount the volume?"

Does the drive fail to appear on the desktop or the sidebar? Does Disk Utility recognize if the drive has been plugged in? Is this a solid state drive or a spinning mechanical drive?

I have a couple of SSDs that mount and show the catalog, but they won't respond otherwise. Very sad, but unrecoverable. I've certainly had HHDs that have died. Now, quite paranoid, I do double backups. Unfortunately, the two SSDs that died were backing each other up.