Do curly braces inside json string objects need to be escaped?
No, curly braces do not have to be escaped in JSON strings.
JSON is defined in RFC 7159. The Section 7: Strings lists the string characters that must be escaped:
All Unicode characters may be placed within the quotation marks, except for the characters that must be escaped: quotation mark, reverse solidus, and the control characters (U+0000 through U+001F).
While all characters can be escaped, curly braces do not have to be.