"knife node environment set ..." is to set the current environment for a particular node, so not what you want here.
To update a cookbook version constraint within a given environment for all nodes joined to that environments, you'll want a "knife environment" command (https://docs.chef.io/knife_environment.html). Depending on the other parts of your environment, there are more comprehensive options.
At the most basic, you can do this with a file. Environments are objects on the Chef server and can be represented as json files, so if you're just starting out with a simple Chef workflow to test, that might be all you need.
"knife environment from file <somefile.json>" will update an environment on your chef server
If you want to see your current environment in json format, "knife environment show -F json"
$ knife environment show dev -F json
"description": "Development Hosts",
One of the tasks in your pipeline would be to create a new version of this json file with the proper updated constraints and then upload it to your server. Depending on just how ugly you want it to be, you can do horrible things with sed.
$ knife environment show dev -F json | sed -e 's/"test": "0.1.0"/"test": "0.1.1"/' > dev_new.json
I wouldn't want you to run that in anything touching your production systems, but you can see what I mean about getting a new version into your environment.
"knife environment from file dev_new.json" would push that back up to your chef server with an updated version of the test cookbook. For a test, maybe that's .. "fine", but there's better stuff out there, depending on what kind of components you have going:
For Chef Automate+Jenkins, there's a plugin https://github.com/jenkinsci/chef-cookbook-pipeline-plugin
There's a Jenkins library: https://github.com/jmassardo/Chef-Jenkins-Library
some of these might also be useful:
You could also look at "knife spork", which is a plugin for knife that was built for cookbook workflows. https://github.com/jonlives/knife-spork
This talk from ChefConf 2019, "Zero to Pipeline" might also be helpful: https://www.youtube.com/watch?v=aaq5X5QvaBk
Over the past several years a number of patterns have emerged in the Chef ecosystem to provide comprehensive testing and integration of cookbooks with the roles/environments pattern and also now with Policyfiles. If you are brand new to Chef, Policyfiles are the way to go; roles and environments aren't going away, but the next generation of features in the Chef ecosystem rely on Policyfiles heavily and replace roles and environments in most functionality. https://learn.chef.io has a set of modules on getting started with Policyfiles.
If anyone else out there has their pipeline code posted somewhere public, please share what you've done!