I was having the same problem since Thursday. None of those annoying "workarounds" (such as alt-tabbing) are realistically feasible. The only solution is to restore to older version. For me it was 64.0.3417.119, before bookmark rework fiasco.
In the recent year or two Opera dev's work had disappointingly poor quality. They keep making poor design decisions, essentially forcing the customers to "eat up" what they came up with, instead of listening to recommendations and suggestions. I do not recall a single useful change since 2019.

My Opera icon on the top-left corner of the browser gets red background. Normally it's a red letter "O" on dark background.
It's not the task bar icon and has nothing to do with broken downloads.
After I close / reopen the browser - the icon gets back to normal for a few minutes, but then it lights up red again.
Seems like it started happening yesterday, or a day before.

@leocg
I does have an option to get the "latest security update" but that links only takes me to Opera download page. Obviously I don't want to use that - I already have the version of Opera that I like. I have "autoupdate" file deleted and all Opera update tasks killed in taskschd.msc
I want to make absolutely sure that Opera does not update automatically. I will only update it manually when I need to. That means I also do not need to see any useless notifications from Opera about new updates.
I don't want to hide the entire side bar for this.

I was having the same problem since Thursday. None of those annoying "workarounds" (such as alt-tabbing) are realistically feasible. The only solution is to restore to older version. For me it was 64.0.3417.119, before bookmark rework fiasco.
In the recent year or two Opera dev's work had disappointingly poor quality. They keep making poor design decisions, essentially forcing the customers to "eat up" what they came up with, instead of listening to recommendations and suggestions. I do not recall a single useful change since 2019.

@andrew84
I thought this flag has been discontinued for over a year. However, I just restarted the browser with this flag and so far the notification is not popping up. I'll keep an eye on it.
Thanks!

@leocg
I does have an option to get the "latest security update" but that links only takes me to Opera download page. Obviously I don't want to use that - I already have the version of Opera that I like. I have "autoupdate" file deleted and all Opera update tasks killed in taskschd.msc
I want to make absolutely sure that Opera does not update automatically. I will only update it manually when I need to. That means I also do not need to see any useless notifications from Opera about new updates.
I don't want to hide the entire side bar for this.

My Opera icon on the top-left corner of the browser gets red background. Normally it's a red letter "O" on dark background.
It's not the task bar icon and has nothing to do with broken downloads.
After I close / reopen the browser - the icon gets back to normal for a few minutes, but then it lights up red again.
Seems like it started happening yesterday, or a day before.