How to keep your seed phrase properly : Write it down in a note , and keep it in safe place (safe from physical attack like water , fire etc) . And put it in a place you can easily remember or access, so that you won’t forget where you put it , because if you lose it you won’t able get it back .
It is quite interesting that I have had few experiences, especially from people's mistakes. One major concern when it comes to the man handling of seed phrase is people's inability to adher to instruction. Because I want to believe that most mobile wallets that we have these days does few things that teaches some basic level of privacy to the user. The few things AFAIK...
It doesn't allow screenshot of seed phrase,
which should be enough reason to raise one's curiosity
It informs a user to write down each word produced, and some wallet go as far as dropping the word one at a time.
It also request for few words out of the 12 for verification purpose at that instance.
And I guess some wallet might emphasize the importance of those words in a very short sentence.
To backup seed phrase online is not advisable.
Well, it's good that the OP corrected the statement, because I have seen a Gmail hack, and the victim resorted to keeping his phrase there before the hack happened. It is clearly not a secure means of storage.