To offer a prepackaged solution based on the Debug-String function, available as an MIT-licensed Gist:
Assuming you have looked at the linked code to ensure that it is safe (which I can personally assure you of, but you should always check), you can install it directly as follows:
irm https://gist.github.com/mklement0/7f2f1e13ac9c2afaf0a0906d08b392d1/raw/Debug-String.ps1 | iex
The primary purpose of Debug-String is to visualize (hidden) control characters and spaces in strings (see this answer), but it also offers the -AsSourceCode and -SingleLine switches, which produce the desired single-line, control-characters-as-escape-sequences string representations (albeit with the enclosing " chars., but you can easily trim them with .Trim('"').
Additionally, you may use -UnicodeEscapes in order to represent non-ASCII-range characters (e.g. é) by their Unicode escape sequences (e.g. `u{e9}), though note that such escapes are only recognized in PowerShell (Core) v6+.
Debug-String -AsSourceCode -SingleLine -UnicodeEscapes 'Tést`1
123'
The above yields (verbatim, including the " chars.), which can be copied and pasted into PowerShell code to expand to the original string:
"T`u{e9}st``1`n123"