I’m curious about what the application domain is and what the two tabs are presenting, because, in my experience, almost every time I’m tempted to use tabs and run into something that doesn’t work smoothly, after I spend more time thinking about the design, I end up deciding tabs weren’t ever really a good UI fit in the first place.
In other words, hitting a situation where stuff you want to do with tabs is hard might indicate that you shouldn’t be dealing with tabs at all, and I’m wondering if that might be the situation you’re in.
To explicate further, the most canonical tabbed UI I can think of is where you have several “mini-apps” bundled together in one. An example would be a dungeon exploration game, where one tab shows the dungeon map, another the player inventory, another a chat window where one can talk to other explorers, and finally a journal of story events. Every single one of those is thoroughly independent of all the others. The player can switch back and forth freely between them, and each tab will be just as they left it the last time it was open.
A situation where I have seen people trying to use tabs that I think is a bad fit would be a product catalog, where we have a “list of search results” tab and a “single product detail” tab. The reason I think this is a bad UX is that it doesn’t correspond to how people typically interact with such an app, which is:
I want to buy a blender. I type “blender” in the searchbar, and get a bunch of blenders. I click on one that looks interesting, and see what details are available to consider when comparing to other options. Now I go back to the list and pick out several other possibilities, and flip amongst them comparing features.
This is impossible, because once I click the second blender in the search results, the “detail” tab switches to blender B, and blender A vanishes, nowhere to be found until I nuke blender B.
Somebody trying to implement a two-tab list/detail pattern would be concerned with “how do I convey which blender got selected out of tab A over to tab B”, which is what your question feels like to me.
If that is indeed the case, I fear that any attempt to directly answer your question (for example, you can shadow anything you would ordinarily do with router parameters with mutually injected services) might only serve to send you further down a path that you might eventually decide you didn’t want to go down in the first place.