When using JS fetch api with the wordpress is set up your issue is with the body.
fetch passes body data in a way that wordpress can’t understand.
Your body: {} should be like this
body: new URLSearchParams({
username: 'thewhitefang',
password: '@bhishek01',
action: 'login_ajax'
})
and you need to change your content-type as well. 'Content-Type': 'application/x-www-form-urlencoded'
I can’t really explain it well because i never really dived deep into this subject but im sure you could find everything you need about this.
Hope this helps =]