If I have multiple server environments that are independent from each other, each running their own app, mysql server etc... do I need multiple SigNoz installations to see them separately?

You could annotate them with environment specific tags and filter them at the view layer this way you don’t need to run multiple SigNoz installations for each env.

Sorry if that's a silly question, I'm quite new to this - how exactly would "annotate them with environment specific tags" work? Add a prefix to the service names?

How are instrumenting the apps and sending the telemetry? Depending on the component, you would add the additional label in the code or enrich at the receiver/processor.

So far I have only installed SigNoz and looked around the example data, but I will be using https://signoz.io/docs/instrumentation/express/