Themes do not use Webhooks, but they are commonly used by apps.

Most app developers will hopefully update their apps automatically before the April deadline (including us, with our Size Chart app), so you’ll probably not need to take any action at all.

If you want to, you can reach out to Shopify to find out which apps might be affected by this update, or you can contact the developers of the apps you have installed directly (each app in your Shopify admin should have support contact details).