[angular-apollo-tailwind]: Update Angular and other deps to latest version  #1884

Is your feature request related to a problem? Please describe.

• The starter currently uses Angular 13.3. We should update it to use Angular 16 and update any other packages to their latest versions in the process.
• After we update the starter, we should update the showcase with the same deps.

The related issue: thisdot/starter.dev#1320

Describe the solution you'd like

Update dependencies to match the updated starter.

Describe alternatives you've considered

Keeping deps out of date.

Additional context

No response