I can't get used to either Twitter or the fediverse, but they don't work differently on the discoverabilty aspect.
One would likely just subscribe to your city's hashtag for large cities or to your town hall's account for small ones, and that's all. The rest works like Twitter (except there is less risk of important posts getting invisibilised by the feed algorithm).
In my fediverse test, I just subscribed to #Antwerpen (as well as #Antwerp and #Anvers but that's a whole other problem...) and I did get relevant and interesting posts. In their small town my parents are subscribed to the town hall's Facebook account (the only reason they signed up to Facebook) and it would work the same on any other app, except it likely would spy on them a bit less. Mastodon's Android app is not a "more custom" app than Twitter or Facebook's apps are, on the contrary I would argue.
I just can't get used to checking this thing more than once every few days and like Twitter it just doesn't work if you're not constantly reading your feed, because then you're missing most posts.