This snippet would do what you are asking:

"Paste Multi-line To Single Line":{
        "prefix": "pasteMultiLineToSingleLine"
        ,"body": ["${CLIPBOARD/(\r\n|\n|\r)/ | /g}"]
        ,"description": "Paste from clipboard replacing every new line with a ' | '"
    }

The main difference is in identifying the different possible line ending characters.

Further explanation of the "body": in case someone else likes to understand the individual parts:

• Parts are separated by /
• ${CLIPBOARD} = Gets the contents of your clipboard.
  See variable reference page [1].
• (\r\n|\n|\r) = This part gets uses regex to get all possible line endings.
  • | = read as 'OR'
  • \r\n = Windows line endings
  • \n = Unix line endings
  • \r = Very old Mac systems line ending. Might be able to do without this one. I'm just in the habit of having all cases covered.
• | = This is the replacement text.
  There is a whitespace on either side of the bar |
• g = regex option to find and replace all 'global' instances and not just the first occurrence.

Reference:

[1] VSCode Snippet Variables: https://code.visualstudio.com/docs/editor/userdefinedsnippets#_variables

[2] Stackoverflow ref1: Match linebreaks - \n or \r\n?

[3] Stackoverflow ref2: Difference between \n and \r?