Recently, I've met several bots in Google TensorFlow git repos.
When I submit a PR, one TF bot finds some related groups for the PR and says, "Can one of admins verify this patch?"
Then, one of a verifier bot says, I need to signup something, and I left a comment, Done. Then, the bot checked and marked it was done.
Then, later one admin commented, "jenkins, test please." I guess this triggers Jenkins and reports the test and other checker results.
How could I setup the (bot)environment and github workflow like this?
You have to learn a continuous integration tool like jenkins. Jenkins has triggers to find such events. After events like below triggered. You can use variety of plugins to accomplish very different tasks.
For example
There are a lot of different plugins for jenkins. See them here.