This is how everyone used to make software, before SaaSS became a thing.
(SaaSS: https://www.gnu.org/philosophy/who-does-that-server-really-s...)
It basically means your software works as intended without an internet connection.
You don't get the "reduced version" without internet, it does exactly what you expect it to and does not complain.
A password manager should be offline first, because what if you need to use a password offline?
> your software works as intended without an internet connection.
1Password works both online and offline. An internet connection is required to sync passwords across devices and to periodically verify the status of an account subscription. Besides that, the application remains fully functional when in an offline state for all intents and purposes.
It doesn't matter what the offline grace period is. The problem is that it's a grace period.
There may be reasons to use 1password, but being functionally equivalent to keepass or such is not something it can claim.
You say fully functional, but can 1Password sync between devices if I don't have internet?
An example: GitHub is not offline first, but git is.
How would you sync between devices without internet except if they are on the same network? Good luck with sharing passwords with family members...
Instead of internet you use local transfer networks, e.g. WiFi, Bluetooth, LoRa, RFID, QR codes, USB, etc.
Bitwarden sometimes has troubles with filling in forms properly which 1password more often does the correct thing saving me seconds / minutes every day.
And open source is a good quality in general.
But software doesn't need to be self-hostable or open source to be offline first.
Being capable of running offline is the most premium feature you can give me.
For example, you can have an app on your phone that is closed source and costs money, but you can still access it without internet.
An example of an "offline first" feature that does not depend on open source or self-hosting is: Can you sync your password database to another device without internet? (A more interesting one you can't even take for granted nowadays: Can the program open if you're offline?)