I\'d like to start a release leveraging the VSTS Rest API defined here: https://www.visualstudio.com/en-us/docs/integrate/api/rm/releases#create-a-release
but I need
Unfortunately, for now it's not able to set variable values when you created a release. This is unlike Build definition for VSTS, variables are allowed to change their values at queue time.
There has been a related uservoice, you could vote for it:
Change release variables' value when deploy a release
https://visualstudio.uservoice.com/forums/330519-visual-studio-team-services/suggestions/16616269-change-release-variables-value-when-deploy-a-rele
As a workaround, you could create a draft release, then update variables’ value ,after that, you can start the release by Modifying the status of a release (active)
{
"status": "Active"
}
More detail info please take a look this similar question: Release Variables through REST API - Visual Studio Team Services