The DTM staging library does not linked with Launch staging. Both are different.
It's up to you, if you really want to replace the DTM staging embed code with Launch staging code. Ultimately, once you're fully migrated to Launch, the DTM staging embed code not work at all until you disabled the DTM property.
You can achieve in simulation way and load the Launch staging functionality in browser with the help of Adobe experience cloud debugger, Go to Tools -> replace the Launch embed code with Launch staging.