Store app knows my password, but won't tell me what it is

[soubeagi]

I recently bought another computer, and now I want to install the Microsoft Store apps I have on the old computer onto that computer. The old computer is willing to tell me the eMail address I used when I signed up for Microsoft Store access, and still allows me to download apps using that account, but doesn't seem to have any obvious way of revealing the password it's using to access that Store account - and apparently, my records from when I first set up the old computer are missing this piece of information. Is there any trick I can use to coax this info out of the old computer so I don't have to reset the password for this account (obviously, it's a good one, if I can't even remember for myself what it is) or establish a new account for the new computer and reconstruct the list of installed apps by hand?

(However, let me be clear: I am not seeking to recover a Windows password. My Windows password is entirely separate from my Microsoft Store password - despite all of Microsoft's efforts to get people to link them. I decided when Windows 8 came out that this was a bad idea, and purposely sought to avoid this. I don't regret this decision in the slightest - even given my current difficulty. I still think the less these megaconglomerates know about me, the better.)

 

[pcgeek11]

Did you use the Microsoft Passport Account to set up the store account? If so that is probably the password you need.

 

[soubeagi]

Did you use the Microsoft Passport Account to set up the store account?

I don't even know what that is. When I set up the old computer, I clicked at the lower arrow in this picture for my Windows account, ...

... and then set up Store access through the Store app (using the Store app itself), for the Store app only. I can't find any images of that screen on the Internet, and can't generate one myself because the old computer is already set up with a Store account, and I don't want to lose that. If there was a way to get the Store app to tell me what the credentials are that it's now using to sign in, I'd be fine.

(And just in case it's not clear, when I say "Store app", I mean specifically "the app people use to get stuff from the Store", not the general sense of "some random app obtained through the Store".)