This "could not decode input as JSON" error indicates that the value supplied in the 'Dropbox-API-Arg' request header could not be successfully parsed, likely because it is not valid JSON.
Please check that you're supplying a valid JSON string in the 'Dropbox-API-Arg' request header. If you're not already using one, we recommend using a JSON library for reading/writing the JSON strings, instead of doing so manually.
You can also use the API v2 Explorer to prototype these calls for you. It will build the header for you, and can even show you the code for making the call.
If something still isn't working as expected, please share the relevant code and output (but please redact your access token).
Thanks for the additional information. I see you have extra \ values in your JSON string. You may have copied those from the command-line curl examples in the documentation. Those are only needed in contexts where you need to escape the subsequent " values, such as in bash, like in those examples, since the " character is already used to start the string for the header parameter for curl itself.
Since that doesn't apply to your PHP context, you shouldn't include them as they'll be sent as-is, corrupting the JSON string. Instead, you'd just want something like: