Recent browsers like Edge Chromium now include a long awaited feature: grouping tabs visually in the tab bar. The feature's not perfect yet in terms of taken space as there's no way to remove the group name and maybe merely use the first tab as bearer of the group contents to keep the tab narrow (as the goal is to save space and have more tabs open (not necessarily loaded) at the same time!).
One of the major issue I have with new tab rules is that they never quite open where I want. Usually, you have to choose globally between opening them next to the source tab or on the far right (that's not even visible anymore due to the single line tab line with navigation).
In my opinion, it would have been more profitable to have a tree-like opening strategy, where new tabs go after all of the direct sons of the source tab.
Workaround with Tab Groups and Mapping:
Well, as this is not happening, maybe tab groups may help.
I'd like to be able to say that certain tabs (like search page: google, duckduckgo, quant...) will automatically open their tabs into a given Search Result group (you have to be able to write a rule for that for the user to type in with some existing preset rules).
End of workaround.
That's only one suggestion actually. I think the future of browser lies in your ability to organize the ever growing number of tabs you might open in a manageable way. Seeing it as a conceptual tree might help to get things right. You should be able to open tabs on a subject among tabs that are about the same subject, whereas the search, which is at the root, will throw new subject roots either just next to the search or at the far right.
Please see hereby attached image. Also, groups may be collapsed, that's the whole point. You might want to extend and have each level be able to be collapsed, expanded so that only a single branch from root to leaf node siblings is open at a given time within a local tree (where that term has also to be defined). Also, the image suggests a single root search page, which might not be the case. Then, things have to be understood on what it means to move a tab in the tab bar: where does it land in the conceptual tree... maybe displaying the tree in 2D at some point might be inevitable.
Good luck!