As stated in Windows App SDK app lifecycle

Windows App SDK apps, like UWP apps, are started and stopped. They are either running or not running. [...] unlike UWP apps, they cannot be suspended and resumed

So if you run your background work in-process, you're fine, depending on what you really need, even a PeriodicTimer is ok.

If you must run out-of-process, the easiest is probably to write another .exe doing your cron work, add it to the package, and declare it as a Startup Task for example:

<Package
  xmlns:desktop="http://schemas.microsoft.com/appx/manifest/desktop/windows10"
  IgnorableNamespaces="desktop">
  <Applications>
    <Application>
      <Extensions>
        <desktop:Extension
          Category="windows.startupTask"
          Executable="bin\MyStartupTask.exe"
          EntryPoint="Windows.FullTrustApplication">
        <desktop:StartupTask
          TaskId="MyStartupTask"
          Enabled="false"
          DisplayName="My App Service" />
        </desktop:Extension>
      </Extensions>
    </Application>
  </Applications>
 </Package>

See here to programmatically enable or disable your startup task: StartupTask example

As for local database storage, as long as you store it in the official package-relative ApplicationData.Current.LocalFolder, it should be accessible by both applications.