PING – Shared To-Dos - Shared to-dos for couples, friends, and families
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PING is a simple to-do app for managing personal tasks and shared tasks with someone close to you. Connect through an invite code, add tasks together, and see updates when either person edits or completes a task. PING also includes due-date reminders, home and lock screen widgets, Live Activities for urgent tasks, and custom lock screen wallpapers. Available in 11 languages.

Replies
shared to-dos with my partner have always been a mess of screenshots, so the simple invite code setup here was a nice surprise. Live Activities for urgent stuff actually seems useful.
The shared list with my partner actually works like you'd hope, no fiddling with permissions or extra accounts to set up. The widgets make it easy to glance at what's due without opening the app, which is the whole point.