In the first case the account is inaccessible for a fair bit of time if either X or Y dies. In the latter case both can always access it.
My partner's aunt got hit by this when her husband was 100% incapacitated and hospitalized. She couldn't even pay her rent or buy groceries, because she couldn't prove her husband agreed with the spending.
We switched our account to the "or" style really fast after that.
If you just have the access permission and the main owner is incapacitated or dead, your access is not valid anymore and it's a huge hassle to get access to the funds.
You want the co-owned style where both have equal rights to the funds on the account. The easiest way to check it is just to contact your bank and make sure it's set up that way the exact terminology seems to vary a bit between banks.
It's much rarer now because checks are basically gone, but you used to be able to get accounts that would require both signatures on the check, not just one.
Fundamentally, the OP isn't faced with a tech problem. People need to start with greater awareness of power of attorney, wills, and probate.
In a probate situation, your loved ones don't have to know all your passwords and so on. They do need to know where your assets are so they can contact the right organisations to claim them. And you can make that process easier for them by avoiding having small accounts all over the place.
I lost all but one of the hundreds of domains I owned, 10 years of email, and of the thousands of online accounts I had when I was locked up, only about 3 were accessible after I got out due to changes in security policies or email addresses (I'm looking at you Gmail) that I could no longer log into despite having the username and password.
This problem is only going to get worse as more sites, sensibly, require MFA. As long as you are compos mentis and have physical access to your devices everything is grand, but once that breaks down, you (or your loved ones) might be screwed.
Then you can give them access to 1Password or similar in some way.
The key point is that the whole process should be far easier if these things are setup in advance, while the person is still able to make their wishes clear, i.e. while they can still say who they trust to make decisions for them.
I imagine if we ever get around to accepting euthanasia as a society the idea around a living will need to become formalised. For decades my dad was very clear he would prefer to be dead than exist in the state he is now but sadly the law insists he, or whatever is left of him, must suffer.
She'd also made my sister and I co-owners on her bank account, so we had no difficulty accessing money for her care in the short term.
His stroke was one of the emotionally hardest times of my life. He had lost language entirely as well - and most movement.
My father had a stroke so debilitating that he lost language entirely, lives in a brain care unit 24/7, and has zero chance of regaining even the most basic idea of a life. But by not being biologically "dead" he retains a lot of legal protections that don't really suit his situation and my mother is unable to sell her home without the permission of the Court of Protection. We filed for said permission 14 months ago.. and, you can guess the rest. With a lasting power of attorney, she'd have been able to organise her life properly within weeks.