It’s in Spotlight now
Since macOS Tahoe, Spotlight keeps what you copy. Press Command-Space, then Command-4, or click the Clipboard button beside the search field. The first time, macOS asks to turn it on.
Using it
Select an item and press Command-C (or click the button beside it) to copy it again, then paste it wherever you like. It keeps text, pictures and files.
How long it keeps things
In System Settings › Spotlight you choose how long: 30 minutes, 8 hours or 7 days. The switch to turn it off is there too, and Clear Clipboard History empties it on the spot.
A word on passwords
What you copy from Apple’s Passwords app stays out of it; passwords copied from other apps might not, so clear the history if you’ve copied something you’d rather it didn’t keep.
When you want more
Spotlight’s history is there when you go looking for it. If you reuse the same few things all day, a clipboard you can see is handier: SideDock’s Clipboard tile sits in a dock, shows what you copied lately, lets you pin the ones you reuse, and never keeps passwords. Click one to copy it again.
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