My way of keeping my mnemonic phrase is I created an excel file on my google sheets, you can find it on your gmail. Aside from that, I also created a copy of it on my computer notepad that was saved on my drive. I also saved on my notebook, all important information and passwords are in there. I always do that incase I lost one of my saved documents. I experienced losing it before, so I learned from it and I feel secured on that way.
I hope you are joking.
Firstly it is very easy to leave a device with your google account logged in, so it would be quite trivial to find your keys.
Secondly, you are exposed to data leaks from Google.
Storing your key online is exactly the only thing you don't want to do.