The PWA module is designed to work out of the box for very general cases without providing too much customizable functionality. People wanting advanced PWA functionality often have too-specific of requirements to wrap it up all nicely in a module, but many folks just want branding and some pages to work offline. PWA can offer those basics to you.
When you install the PWA module, you should get a Web Manifest and offline caching, provided you specify which URLs you would like cached in the admin settings. The Web Manifest also works with almost no configuration, but if you want custom icons you can implement
hook_pwa_manifest_alter() (link goes to official example) and specify your own icons.
If you have any specific questions the best way to get support is by filing an issue on drupal.org and labelling it as a support request. I typically respond quickly and try to point you in the right direction even if I can't offer a coding solution.
I would also love to document your experience in terms of how it works with CiviCRM, and if necessary we can offer recommendations on URLs to exclude, assets to cache by default, etc.