How do you find legacy system extensions?

I don't know of a way to specifically find "legacy" system extensions; however, if you're looking for the extensions mentioned by the OS dialogs warning you about their deprecation, you can run the following in Terminal, noting the lines beginning with Signed by:

system_profiler SPExtensionsDataType

For example, macOS told me this morning I had a legacy extension signed by "Ploytec GmbH." Note the last line in the output below:

    TASCAM_US1800:

      Version: 3.00d8
      Last Modified: 2013-12-06, 08:52
      Bundle ID: com.tascam.us1800.driver
      Notarized: No
      Loaded: No
      Get Info String: US-1800 Driver Version 3.00d8 (build 3877)
      Obtained from: Identified Developer
      Kind: Intel
      Architectures: i386, x86_64
      64-Bit (Intel): Yes
      Location: /Library/Extensions/TASCAM_US1800.kext
      Kext Version: 3.0.0
      Loadable: Yes
      Dependencies: Deprecated
      Signed by: Developer ID Application: Ploytec GmbH (348SCJ68PR), Developer ID Certification Authority, Apple Root CA

If you are running Catalina 10.15.4 and are referring to the popups, they are just to let you know kexts will be deprecated in the next version of macOS. I don't know if there is a way to find them currently. Nothing to be concerned with.

Worried about if it will run in Catalina? Go to Apple menu -> About This Mac -> System Report -> Applications.

It tells you what is 64 bit or not. There is a great App called Go64 that scans for legacy code too.

Extensions?

How Legacy?

Extensions generally should only be installed as prebundled with the operating system.

The only difference is extensions from pre-2002 Mac OS 9 and earlier systems.

Those you might be able to find through resources on http://www.lowendmac.com/

What are you trying to accomplish?

dialabrain has the reason covered. If you want to see where they are, all third party kernel extensions are in this folder:

/Library/Extensions/

That's the root Library folder, not the one in the System folder, or your user account. There's also 10 default .kext files the OS installs to this folder.

I'm not technical but when I see that some legacy kernel extension(s) may stop working because they aren't going to be supported in the future, I become interested in knowing if something I am running will stop running in the future. That's why I'm also interested in knowing where and how to find them. If OS is smart enough to give me the message, can't it be smart enough to tell me what is on my machine that I should followup on?

Writing an effective Apple Support Commun… - Apple Community