No_Shorty, once again: the forum has an attachment feature. Please us it, instead of 3rd party services.
The image now works, but it doesn’t give the answer to what I asked you earlier about running batteries in sequence. You never addressed that, even despite others also asked you about this. You
mentioned batteries above, but this is really just repeating the same statement. A description of how you want it to work, without explaining why you want it this way. And it’s focused on physical appearance and being (or not) in the same enclosure, while we ask you about a completely unrelated thing: the behavior of the circuit.
My guess is that you are focused on some particular picture, which appeared in your head, but you never questioned its sense. So please stop for a moment and rethink it.
Under constant current discharge there is not difference in how long the load will be powered in either scenario:
Even if the backup battery is smaller (2:1 for this illustration).
If it’s not constant-current discharge (e.g. a linear load), there will be some difference, though which will win depends on the situation.
I’m not saying that there certainly is no advantage or no reason to run them this way. There may be. But implementing all this without a good reason is a waste of time and money, making everything less reliable, and even causing a slighly higher energy losses. This is a forum and people try to provide best advice, hence the questions.