profile: Display user's local time

[sirpengi]

In the profile screen (#195 ) we should show the current time in the user's configured timezone. This will involve integrating timezone data.

We've identified https://pub.dev/packages/timezone as a good candidate (chat thread) and an initial attempt was already made to integrate it, but the initialization of the database was measured to take ~100ms during bootup. It would make sense to delay the initialization of the database until we need to display the profile screen.

A followup issue will be:

• #293