If I want notifications from a tab, I pin it. I think that pinned tabs are already a bit more aggressive about keeping that website "active", and it's always on the tab bar no matter how far you scroll. So for my use case at least, the suspender just has to not suspend any pinned tabs.

> I think that pinned tabs are already a bit more aggressive about keeping that website "active"

Just not... around.

Routinely, after both clean shutdowns and system crashes, firefox just loses all my pinned tabs. It's the primary thing that keeps me from using firefox as a default all the time. There's weird 'restore last session' and folder searching you can do to try to maybe 'recover' some, sometimes, but... WTH? I'm pinning things - I want them around. If I didn't want them restored on browser launch, I wouldn't 'pin' them. Unless pinning is intended to be transitory, and I just missed the memo?

Never had it lose them for me in an extremely long time. Restore last session has always happily recovered them too, if necessary.

sometimes 'restore last session' doesn't even come up when loading up. :/

It might be too late for you to see this, but this is an option in the hamburger menu, even if no pop-up window shows up when you start Firefox.

I'm using pining many years and they have been persistent so far. Crashing and losing all tabs is a risk though, but it was a long time ago.

And I imagine that some websites might do things that take a long time, like a heavy upload, download, or something that takes a lot of processing (e.g. loading a game). In those cases, I would think that people would rather just have them keep working in the background while they focus on other stuff.