To encode you can utilize the built-in @base64 operator:
$ echo '{"data": "Hello World!"}' | jq -r '.data | @base64'
SGVsbG8gV29ybGQh
To decode you can utilize the built-in @base64d operator:
$ echo '{"data": "SGVsbG8gV29ybGQh"}' | jq -r '.data | @base64d'
Hello World!