How am I supposed know what software will and won't be compatible?

Are you asking because of a "legacy extension" warning? You need do nothing. See:

About legacy system extensions - Apple Support

 If you still feel a need to see what they are, do "About this Mac..." from your Apple menu and, in the resulting window, click the "System Report" button. That opens ite built-in utility, "System Information."

In that app's left-hand pane, scroll down the left pane to "Software" and, if needed, click the little arrowhead to expand the section. Find "Extensions" (see below) and select it.

Now you get to wait. The extensions info is a slow load. Have a good stretch. Once they display, click the "Obtained from" column heading to sort by the developer. 

We can assume Apple will deal with theirs. That leaves a few from other developers, Some are used internally by Apple so we can expect them to be compliant in time for the changeover as well. The Logitech web page says their software will be compliant by the time the changes required.

Even with this info at hand, you still need do nothing.

Whoever are the developers or purveyors of the individual software application. We don't know who that would be. See App Compatibility Table - RoaringApps.

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Generally, the alert should tell you which apps are using deprecated system calls, and that should give you an idea of who to talk to - start with the web site of the app in question.

You can also use System Information.app to get a list of all installed applications - this will also give you an idea of where they came from - e.g. 'Apple', 'Identified Developer', 'Mac App Store', etc.

Apple should keep their own software up to date, so they're unlikely to be a problem.

'Identified developer' should show the name of the developer, which may help track down their support

'Mac App Store' apps should be automatically updated (assuming you have this enabled), and you can use the App Store app to find the developer information if you want to reach out to them directly.