If you haven't already used the ".new" domain shortcuts with Google's G Suite services like Docs, Sheets, or Slides, you're missing out. The feature allows you to quickly and easily create a new blank document (or spreadsheet, or presentation, etc.) without all the tedium of navigating Google Drive to open one. The only real disadvantage was they would previously only open a new document under your current primary Google account, but now you can append a number (i.e., docs.new/2) to open a new blank document under a different account listed in the switcher.
— G Suite (@gsuite) July 25, 2019
The feature change here really is that simple. Just add a slash and a number after the shortcut URL you are using to have a new document opened in a different account. In my testing, the numbers you need to use correspond to how they are listed in order from the account switcher when in your primary account. (Note that is inconsistent with how Google enumerates users in the URL when in Gmail, for some reason.)
The "R" avatar account in the switcher here would correspond to docs.new/3 if using the domain shortcuts.
Now the next time you need to quickly open a new document on a non-primary account, just remember to append a number to the end of the .new shortcut. Hopefully, you can remember which accounts get which number.