[ETA: Since we're in the new days of a new place perhaps I should be less laconic. I have been arysteia on a million platforms for at least 22 years now. If you've ever known me anywhere else, yes it's me.]
Works just like the mobile app.
Install this app on your iPhone: tap the share button and then Add to Home Screen.
Tap the Share button
in Safari's toolbar
Select "Add to Home Screen"
from the menu
Tap "Add"
The app will appear on your home screen
Enter your Bluesky handle and app password to unlock posting, likes, and your Following feed.
Need an app password? Open Bluesky, go to Settings > App passwords, and create a new one.
Sign in with your Bluesky account to unlock posting, likes, and your Following feed.