Azure pipeline branch name for build and release

I am trying to setup a Azure Devops build and release pipeline to build and deploy a Databricks job using Databricks assets bundle. I have been following the following Documentation: https://learn.microsoft.com/en-us/azure/databricks/dev-tools/ci-cd/ci-cd-azure-devops

The build pipeline is a simple one as given below which is triggered on merges to main and develop branch.

trigger:
  branches:
    include:
      - feature/azure-pipeline

pool:
  vmImage: ubuntu-22.04

steps:
- checkout: self
  clean: true
  fetchDepth: 1
  persistCredentials: true


- bash: echo $(Build.SourceBranch)

- task: ArchiveFiles@2
  inputs:
    rootFolderOrFile: '$(Build.SourcesDirectory)'
    includeRootFolder: false
    archiveType: 'zip'
    archiveFile: '$(Build.ArtifactStagingDirectory)/$(Build.BuildId).zip'
    replaceExistingArchive: true

- task: PublishBuildArtifacts@1
  inputs:
    ArtifactName: 'DatabricksBuild'

Now, in the release I have an env variable which will depend on the branch which triggers the build. How would I save the triggering branch name in build pipeline to use it in the release part of the pipeline?

As far as I understand, your requirement is to retrieve the branch name within the release pipeline; the commits/merges into this branch trigger the upstream build pipeline, which then produces artifacts and triggers the downstream release pipeline.

For this, you may directly use the Predefined Variables of $(Build.SourceBranch) and $(Build.SourceBranchName) in your release pipeline; Azure Pipelines populates such variables for the designated primary artifact.

If you added multiple artifacts generated by different build pipelines, you may also use $(Release.Artifacts.{alias}.SourceBranch) and $(Release.Artifacts.{alias}.SourceBranchName) to get each triggering branch of different build pipeline artifacts.