Suppose I wanted to embed your solution itself into a template literal. It would look like this:
`${'`'}Look, this is a backtick: \${'${'`'}'}${'`'}`
`${'`'}Look, this is a backtick: \${'${'`'}'}${'`'}`
r"foo" == "foo" // r" means the literal ends at "
r#""foo""# == "\"foo\"" // r#" means the literal ends at "#
r##"r#""foo""#"## == "r#\"\"foo\"\"#" // r##" means the literal ends at "##
Basically you add as many # outside as necessary to distinguish the end of the literal (double-quote followed by some #) from any such sequence in the middle of the literal.