Anne McCarthy has published a YouTube video that explains what’s going to happen with the Customizer once WordPress 5.9 ships. The short answer is, it depends on the theme. If you’re using a theme that utilizes the customizer already, nothing will change. If you use a Full-site Editing theme, the Customizer disappears in favor of the Site Editor. And if you want to use the FSE but still have access to the Customizer, check out a Universal theme.
By the way, this post on the Make Core blog goes into a bit more detail into the changes concerning the Customizer and Full-site Editing themes.
One thing is certain. WordPress 5.9 is the beginning of the end for the Customizer. It will likely be deprecated at some point in the next two to three years. By that time, Full-site Editing will be able to do everything the Customizer can do and a whole lot more.