You should ask questions like this on the win-acme github page but from my understanding the actual details of the renewals are held in C:\ProgramData\win-acme\acme-v02.api.letsencrypt.org\*.renewal.json
Your other server will need a different certificate unless you are trying to load balance the same name.
I would also recommend you check out my app https://certifytheweb.com if you are looking to automate a bunch of certificates/services. It does the same things but in a more easy to see way.
Sorry I'm not an Exchange administrator so I don't know the details. If all servers will have the same certificate then use once machine to get the certificate then use scripting to deploy to the other servers.
Most of the popular Let's Encrypt tools support scripting so that you can run your owns scripts when your certificate has renewed.
For instance, for Certify If you already have a working script you can adapt it to be a PowerShell Script deployment task. See https://docs.certifytheweb.com/docs/script-hooks - the specific actions you need to perform will vary depending on your services and the environment you are deploying to. There usually isn't one re-built script you can run that just does it all although there are many you can adapt.
Here is an example script by another Certify The Web user: