Well tau pretty much covered everything that I have/would recommend for iOS.

However, I do have a couple additions.
For photo/video, I have switched from Snapseed/Lightroom to
Polarr for my main mobile photo editing as it offers more granular editing, especially with HSL sliders (which are a paid feature on Lightroom and absent in Snapseed). However, iOS 13's photo editing has been revamped and is pretty amazing. In actually taking photos, the iOS camera app is great, however for manual control I personally would recommend
Halide and
Moment (although these have become paid apps/more expensive since I've gotten them). In video editing,
iMovie is a great free option, as well as
InShot for making really quick, simple videos (usually for social media).
For simple graphic design,
Canva and
Adobe Spark are great if you need to design a quick poster/flyer/icon/social media story/etc. on the go.
I also highly recommend
Libby and
RBDigital for reading. All you need is a library card, and you have access to a plethora of books, audiobooks, magazines, and newspapers for free!
For weather, I personally use
Dark Sky for its freakishly accurate precipitation forecasts.
I use
Todoist as a task manager, recently switching from Any.do (and before that Reminders, although iOS 13 Reminders has been rebuilt from the ground up) for its natural task input integration. However, the free version of Todoist lacks some features that Any.do offers for free. I also use
Google Calendar and everything else Google (Gmail, Google Drive/Docs/Sheets/Slides, Google Maps, Google Assistant, Google Photos, Snapseed, etc.).
Scannable is a handy app for scanning documents into PDFs or images.
Other than that, I use
Vellum for wallpapers (although the wallpapers I use now are all self-shot) and
Spotify for music, along with basically everything else tau mentioned.