TL;DR: App A said I needed App B but App B said it needed authorization from App A first, solved by closing a full-screen popup from App A pointing me to App B, which then revealed in App A the code I needed to authorize App B.
Note: original issue is still unresolved, trying to play Diablo 2 Resurrected on my desktop PC because I haven’t played in the last 30 days and I’m still stuck in that loop, but this tale is of the absurdly winding, unending rabbit hole that Blizzard sent me on while trying to solve that.
29-Apr 0715hrs EST or so, and I decide I want to play some Diablo 2 Resurrected (D2R). Run D2R. See “Press Any Key To Continue”, do so. Accept some settings around gamma, accessibility, and skip the Lord of Destruction (LoD) cinematic – that was my first sign something was off, I shouldn’t have received that having completed LoD a year or so ago.
At the D2R title screen it says “Connecting to Battle Net”, and then says “You have not been online in the past 30 days. Please start the game while online to check for any login agreements.”
I am online, the Battle Net Launcher app on my Desktop shows I am. So I end it and re-start the app. This time my desktop Battle Net Launcher required an update. Sure, update it.
Now it wants me to re-login because my session has expired, and it prompts me with OLD CREDENTIALS. We have Email Address-A (Email-A) and Email Address-B (Email-B). I swapped from my long-time Email-A used from 2004-2021 to my newer Email-B in 2022, if I recall correctly. What is the desktop Battle Net Launcher app doing asking me for my old email to authenticate with? It wants me to approve logging in with my Mobile Authenticator app (M-Auth app). And we’re off to wonderland! 
The M-Auth app starts up and says it’s moved to live within the NEW Mobile Battle Net application (M-BNet app). Okay, let’s install that on my iPhone. Installed. The M-BNet app insists I authentic it with… the time-sensitive code from the M-Auth app. So I go back to M-Auth and it’s saying it now lives … in… the … the M-BNet app…
So I do this dance back and forth for a while trying to figure out what edge case sad path I’ve discovered and how to dig myself out of this lightless hole. I’ve main’d a Dwarf in WoW since 2004 so I’m in-character-convinced digging down will result in a way out. Dwarves. I follow the directions, back and forth, three times, wondering if this is the definition of insanity or if … *AM I THE PROBLEM? Would dual-wilding pick-axes will be faster?
On Round 4 (Fight!) I realized the M-Auth app directing me to install the new M-BNet app was a pop-up screen, with an “X” unintuitively in the top-LEFT corner. Call me brainwashed by the PC master race but I’m used to the “X” being in the top-right corner. It was there in the left all along and I saw it but it didn’t register in my brain, the same way I’m caught off guard whenever the “Exit”/“Cancel” button in a series of menus you want to back out of are not in exactly the same location so you can button-mash instead of have to move your mouse around to find the new location of the previous “Exit”/“Cancel” button.
“X”-ing out of the M-Auth app’s pop-up revealed a fully working M-Auth app with… the required approval code I could Accept, thus authorizing the M-BNet app to complete its setup. NOW my DESKTOP BNet Launcher app was satisfied and I could finally try out the next infinite loop trying to play D2R.
But that tale is for another thread.
Know that I am grateful to the designers across all these apps who come up with smooth happy path journeys I have come to know and love Blizzard for. Know that I see you otherwise-invisible Producers who map dependencies and gantt-chart timelines with features across the myriad of product teams, hand-in-hand with the always-understaffed-yet-secretly-beloved release managers who pull these features, screaming and kicking, into the bright production environment wilds. And thank you, thank you, THANK YOU to the QA Army who discover then laser-target bugs for deadly developers to squash with their heavy hammers, swift swords, and orbital obliterations.