Auto Increment version number in iOS application using Azure Devops

You can achieve that by implementing a script step before building your app.
This script would use the PlistBuddy tool to read and increment the version numbers (assuming you're using a macos machine on Azure DevOps).
I'm also assuming you're using a semantic versioning system major.minor.patch as described here.
This script should get to increment the version number as you described and then write it to the Info.plist file of your app. Note to change the path to that file if you have it differently in your project

- script: |
    buildPlist="$(Build.SourcesDirectory)/Info.plist" # Enter the path to your plist file here
    maxSubversionNumber=99 # Set what will be the maximum number to increment each sub version to

    versionNumber=$(/usr/libexec/PlistBuddy -c "Print CFBundleShortVersionString" "$buildPlist")
    majorVersion=`echo $versionNumber | awk -F "." '{print ($1 == "" ? 0 : $1)}'`
    minorVersion=`echo $versionNumber | awk -F "." '{print ($2 == "" ? 0 : $2)}'`
    patchVersion=`echo $versionNumber | awk -F "." '{print ($3 == "" ? 0 : $3)}'`
    if [[ $patchVersion -ge $maxSubversionNumber ]]
    then
      patchVersion=0
      if [[ $minorVersion -ge $maxSubversionNumber ]]
      then
        minorVersion=0
        majorVersion=$(($majorVersion + 1))
      else
        minorVersion=$(($minorVersion + 1))
      fi
      else
        patchVersion=$(($patchVersion + 1))
    fi
    newVersionNumber=`echo $versionNumber | awk -F "." '{print '$majorVersion' "." '$minorVersion' ".'$patchVersion'" }'`
    /usr/libexec/PlistBuddy -c "Set :CFBundleShortVersionString $newVersionNumber" "$buildPlist"

If you want to keep $(MARKETING_VERSION) in Info.plist for CFBundleShortVersionString but want to increase version after successful archive or build then use following script following script will increase like 1.0 to 2.0 but ofcourse that logic can be modified using @Jobert's solution etc

Script to increase app version in Xcode >= 13