Start with the main task
Before adding progressive web app features, decide what visitors need to accomplish. A booking tool, a catalogue and a game have different needs when a connection becomes unreliable.
A PWA uses web technologies and can add capabilities such as installation and offline access. Those capabilities need to be designed and tested; calling a website a PWA does not make every feature work offline.
Decide what to keep available
List the content people should be able to open without a connection. Separate that from actions that require fresh information or a server response. Show a clear message when an action cannot complete, rather than leaving a button apparently broken.
Test the difficult moments
Check the first visit, a return visit, a lost connection and an update to a new version. Test the browsers and devices your audience uses. A reliable core journey is more useful than a long feature list.