It’s not coming from json, as shown by str() being equally as slow.
Anyway, here are the int results:
$ python -m pyperf timeit --fast -s 'from json import dumps; x = [3141592653589793] * 100' 'dumps(x)'
Mean +- std dev: 17.8 us +- 0.8 us
$ python -m pyperf timeit --fast -s 'from orjson import dumps; x = [3141592653589793] * 100' 'dumps(x)'
Mean +- std dev: 4.88 us +- 0.08 us
$ python -m pyperf timeit --fast -s 'x = [3141592653589793] * 100' 'str(x)'
Mean +- std dev: 15.1 us +- 1.0 us
(So perhaps a little room for improvement in int-to-string, but not nearly the problem of float-to-string.)