After starting to cross-post to Mastodon, I realized that I don't like the default iOS app very much.
I stumbled across a review of many other options (https://transponderings.blog/2022/05/21/eight-mastodon-apps-for-iphone/) and finally switched to "Toot!" (https://apps.apple.com/us/app/toot/id1229021451).
It's great and feels a lot faster. In contrast to others, this one is not free though, I paid $4.