Use the -Raw parameter of Get-Content to match across multiple lines.
By default, Get-Content returns an array of lines from the file.
Example (from PowerShell 7) showing only adding the -Raw parameter returns what you expect:
Get-Content test.txt -Raw |% {$_-replace "t`r`n", "ting`r`na "}
testing
a message
Explanation quoted from Get-Help:
❯ Get-Help Get-Content -Parameter Raw
-Raw <System.Management.Automation.SwitchParameter>
Ignores newline characters and returns the entire contents of a file in one string with the newlines
preserved. By default, newline characters in a file are used as delimiters to separate the input into an
array of strings. This parameter was introduced in PowerShell 3.0. Raw is a dynamic parameter that the
FileSystem provider adds to the `Get-Content` cmdlet This parameter works only in file system drives.