Wasn't sure where to post this, as it has both an iOS, iPadOS, and macOS version. Decided on here, but let me know if that was a bad choice. That's the same reason I didn't make an app entry for it yet.
Was browsing the App Store a few days ago, and happened to come across Spring for Twitter. It's a truly premium Twitter client for the Mac, iPhone, and iPad. The full version costs $9.99, and the light version (for iPhone only) costs $3.99. This may seem a bit pricy, Until you discover some of what it offers.
For one, it has a notifications tab, just like the official Twitter app. I have no idea how they managed to pull this off, but it's awesome! You get notified of likes, replies, etc.
If you're running the Spring 3 beta, you also get customizable push notifications. Granted, they're delayed by like a minute or 2, maybe around 4 for direct messages, but that's much better than some other clients. And you can choose what kind of notifications you want. So if you only wanted to get notified of replies? You can do that.
Spring is also optimized for accessibility. You can rearrange VoiceOver actions, customize your tabs, and a lot more.
It's also the only Twitter client I've ever seen with position syncing that actually works across devices. I can be reading on my phone, go to Spring on my Mac, and no matter if it was already open or not, I'm exactly where I was on my iPhone.
The only real issue that I have is the lack of keyboard shortcuts for a lot of actions. We contacted the developer about this though, and they said they'd look into adding more.
All in all, I love this client. It's now the only one on my phone, and Mac. Here's the App Store link: https://apps.apple.com/us/app/spring-for-twitter/id1508706541