Is it necessary to escape a backslash in a config file

C# and JSON are different languages with different syntactic rules (after all, JSON doesn't look much like C#), albeit their rules regarding how strings look are kind of similar.

Since you're dealing with a JSON file, C#'s rules for strings (verbatim strings in particular) don't apply, but JSON's rules do. In those rules you have to escape a backslash as \\ every time. There is no other way. Otherwise the sequence \t actually means Tab, as you noticed.

There is no real way of fixing this after the fact. Depending on the character after \ you'd get something, like the Tab, or get a parsing error when trying to read the JSON file. While you could turn Tab back into \t if you know you're dealing with file paths I wouldn't recommend it. As mentioned, if the character after the backslash isn't a t, you might get an error anyway without a chance to recover.

As for your attempt of “escaping” the wrong version on the C# side: @ has different meaning, depending on where it's used:

• @"string" is a verbatim string in which almost anything can be written verbatim without having to worry about escape characters. The only exception is "" for double quotes inside the string. But indeed, it's most commonly-used and handy for things like file paths on Windows and regular expressions, both of which are rather annoying to type when having to escape every single backslash.
• @name makes any keyword or other name a valid identifier. You can prefix every identifier with @ and this would make a valid program slightly longer, but doesn't change anything about its semantics. It's purely something for the compiler, similar to, e.g. using directives.

While both features use the same character and have somewhat comparable ideas, they don't work the same and of course, both have no impact at runtime. They're merely for the compiler.

In addition to @Joey's excellent answer, for paths you could use forward slashes:

{
  "MyPath": "c:/testmypath"
}

This is usually pretty well supported. Or to be super safe, you could just revert them back to regular backslashes:

return configuration["MyPath"].Replace("/", @"\");