Might not be what you're looking for but I love SideBerry

Tree Style Tab is great aswell, but SideBerry feels smoother and also has an option for groups

Maybe Panorama Tab Groups? It's not like how Vivaldi does it, but doesn't use the sidebar.

Tiled Tab Groups is similar to Simple Tab Groups, but better imo in some details.

You're looking for something limilar to tab stacking, but said you don't want to use sidebar... But the closest to tab stacking is using an extension that organizes your tabs in collapsable tree structures, like Tree Style Tabs and Sidebery.

I use is Sidebery because I like vertical tree tabs and Sidebery is better than using Simple/Tiled Tab Groups + Tree Style Tab, I know because I spent a couple of years using this combination before switching to Sidebery.

Screenshot of my Firefox. You can see I have four groups with 110+5+68+82 tabs. There are tree pinned tabs visible no matter what is the current active group. Then there's the list of tabs below.

I've looked for something like this as well but found nothing :/ (only simple tab groups)

I'm surprised firefox containers don't have an equivalent feature yet

Do any of these extensions work on Android? It's the one thing I miss from Chrome mobile at this point.