Once your message has been accepted and the builder has started, closing the editor tab or putting your laptop to sleep does not cancel the server-side job. You do not need to leave your computer awake.
If your connection drops before the message is accepted, it may not have been sent. Reopen the chat and check whether your message appears before sending it again.
When you come back
Open the same app and read the latest chat status and reply. Check Version History and Preview before publishing. A run can fail or stop for reasons unrelated to your browser, so closing the tab is not a guarantee that the work will finish.
If the run is still working, wait. If it has stopped, read its explanation before retrying. A missing new version alone is not a reason to send the same request again: first check whether a run is still in progress.
Your published app runs independently of your laptop. Closing the editor does not take it offline.