I think that the closest thing you will find to PastePal is CopyQ.
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KDE Connect can get you most of the way there, unfortunately you won't be able to auto sync the clipboard from the phone to the PC due to an Android limitation (the other way around works instead), but you can still manually send it over. For example, to make it easier to access, I added the tile for sending it in the quick settings
Like you mentioned KDE Connect will sync your clipboard between Android and KDE. The KDE clipboard also has a history and you can run actions on clipboard entries which is super handy. I'm not sure about this snippets library, sounds like a permanent clipboard history that you can search, where the KDE one just keeps the last X copied things. I'd rather have my phone keyboard learn words I type a lot personally.
sounds like a permanent clipboard history that you can search
that's exactly what PastePal is, and what I'm looking for
I use cliphist with rofi. This hyprland wiki has a few wayland cliboard recommendations. Clipse is also good if you don't like how rofi or similar stuff look. But they won't sync fully with kdeconnect. Only the last copied will sync.
in my searching I found XClipper, but unfortunately it's windows only on the PC side

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