Search inputs are synced accross applications, how to disable?
Search input uses the same 'hidden' copy buffer that unix uses in Terminal, called the 'kill ring'. The 'kill' command has a second part, called 'yank'

These are used on text editors/terminals/emacs etc using  Ctrl ⌃   K  &amp;  Ctrl ⌃   Y 

In effect they are copy &amp; paste, they just save to a different buffer than the regular. As far as I'm aware you cannot disable them, only replace the content with the next 'kill', the same as the regular  Cmd ⌘   C  &amp;  Cmd ⌘   V  copy/paste.

How to Geek has a good explanation of how to use it, though not hot to disable it.
How to Use macOS’ Built-In “Kill and Yank” as an Alternative Cut and Paste