Multiple separate triggers in azure-pipelines.yml

If I understand your request correctly, you can achieve this in a single azure-pipeline.yml. Please check below example yml.

trigger:
  branches:
    include:
    - master
  paths:
    include:
    - client/*
    - api/*

jobs:
- job: getchangepath
  pool:
    vmImage: 'windows-latest'
  steps: 
  - powershell: |
      $url="$(System.CollectionUri)/$(System.TeamProject)/_apis/git/repositories/$(Build.Repository.ID)/commits/$(Build.SourceVersion)/changes?api-version=5.1"
      $result = Invoke-RestMethod -Uri $url -Headers @{Authorization = "Bearer $(System.AccessToken)"} -Method GET
                       
      $changesFolder = $result.changes | Where-Object{$_.item.gitObjectType -match "tree"} | Select-Object -Property {$_.item.path}
     
      foreach($path in $changesFolder){
        if($path -match '/client'){
          echo "##vso[task.setvariable variable=Client;isOutput=true]$True"
          break
        }
      }

      foreach($path in $changesFolder){
        if($path -match '/api'){
          echo "##vso[task.setvariable variable=Api;isOutput=true]$True"
          break
        }
      }
    name: MyVariable

- job: client
  pool :
    vmImage: 'windows-latest'
  dependsOn: getchangepath
  condition: eq(dependencies.getchangepath.outputs['Myvariable.Client'], 'true')
  steps:
  - powershell: echo 'client job start'
  
- job: api
  pool :
    vmImage: 'windows-latest'
  dependsOn: getchangepath
  condition: eq(dependencies.getchangepath.outputs['Myvariable.Api'], 'true')
  steps:
  - powershell: echo 'api job start'

In the above yml I have three jobs. In the first job getchangepath I call git get changes Rest API in the PowerShell task to get the changed path which triggered the build. It also outputs the variables if the path contains path /client or /api.

Job client and job api depend on job getchangepath and will be executed on the condition of the output variable in job getchangepath.

Suppose I changed a file in folder client and commit the change to Azure Repo. Then after job getchangepath is finished. MyVariable.Client will be set to true. Then Job client will evaluate its condition and get started. Job Api condtion will be false, and gets skipped.