While our “Deploy to IIS” step does not support this out-of-the-box, you could configure the “Custom Deployment Scripts” feature on the step and consider scripting this with PowerShell.
There are also some community step templates for IIS that may give you more options, or you could even use these as inspiration for scripting/setting your own start mode with PowerShell. For example, this community step has a Start Mode parameter (AppPoolStartMode), and if you click the “Show script” link and inspect the PowerShell code, you can see how it’s setting the start mode.
You could modify this script accordingly and experiment for your needs. Something along these lines may work (untested) - Note the TODOs you’d need to replace throughout the code: