Each person has their own method, but I also really like the traditional way, writing them down on paper and then backing up many copies to store in many places and sharing with the closest people is indispensable.
Keep in mind when you're share your seed phrase to closest people, you're taking a risk they will make a silly mistake to keep/save the seed phrase because their knowledge might be less than you.
What I did was simply encrypt it in a secure box and save it on a laptop that I no longer use and as a backup I saved it in a secure file on Box.com. I think that this is quite safe, considering that it is encrypted, and I also put some of my assets on the exchange, so that even if I lose access to my wallet I still have backup funds on the exchange.
You're trusting your seed phrase over third party, I don't think it can be said as
safe regardless it's encrypted or having password.
The chance you lose your funds is higher in online e.g. centralized exchange than in offline.