Open the Bill or the Bill Payment Check; use Ctl H = the History icon at the top. This shows what is linked to which other transaction. You can use the GO TO, from here.
When you enter a bill, you Parked that you owe for water or office supplies and are not paying now; you intend to Pay Later. Later = Pay bills. This means you Parked the amount owed as generic AP value for that name, and later, you pay the AP value for that name. That's why banking shows Paid AP. Not Paid that expenses detail.
Using the Register is not the View of your data; it is the Access point to these transactions. Your P&L on Cash Basis will show the expense details as paid for the Payment date. On Accrual Basis, it shows as the date of the bill, even if never paid. That's why there are the two perspectives.
If you already paid for office supplies by debit card, there is no Bill to enter first. You already paid. Go straight to Banking menu > Write Check.
If you already paid for office supplies by using the credit card, there is no Bill to enter first. You already paid. Go straight to Banking menu > Enter Credit Card Charge.