The important thing to understand is "clearance and settlement". Banks either maintain accounts with each other ("nostro/vostro accounts") or, within a country, at the central bank. So e.g. Halifax and Monzo will have accounts at the Bank of England.
Settlement will either be immediate or delayed. For immediate, at the same time as Halifax is sending a "please credit £10 to Bob" message to Monzo, they will send a message to the Bank of England to transfer £10 between their account and Monzo's.
For delayed settlement, the banks wait until the end of the day, add up the total money in each direction, subtract the difference, and transfer that.
A lot of work goes into making sure all the necessary entries line up. So, in the example, if the bank sent a payment message but didn't debit their user's account, either they would have made the central bank transfer (in which case they've lost £10 and effectively given it to their user's account), or they haven't, in which case Monzo will notice and demand payment for the discrepancy.
Banking is eventually consistent, and has been for centuries.
The recipient bank will receive the money into their settlement account at that time. If the sending bank doesn't debit their customer then both sending and receiving customers will have the money in their accounts, but the sending bank will be out of pocket.
The standard money transfer from Bob to Joe is a deal where the bank says "ok, Bob, we owed you $100 but if you want that then we'll now owe that $100 to Joe instead".
It's also worth noting that's just a record of debt not reality - there has to be some legal basis for that transaction to actually change the liability between the bank and the account holder, simply changing the balance in a database doesn't change the amount of debt but just the record i.e. "bank's opinion" of that debt; and if that record/opinion is wrong, then that balance can and will be disputed, and if the dispute can't be resolved otherwise, then it'll be up to courts to decide if that debt is valid or not.
If you record just the credit without the debit, then it's the equivalent of the bank unilaterally agreeing to new debt, the bank asserting that it now owes $100 to Joe just because. It's free to do that, but it would mean that it's "books won't balance" i.e. their accounting isn't consistent with itself and doesn't match reality, so to properly account for that transaction they'd have to book a debit to their profit&loss statement since they lost money by acknowleding that balance increase i.e debt without an offseting balance/debt decrease to someone else.
The settlement process through a central bank is a way of ensuring that banks dont need to literally send truckloads of cash to each other at the end of the day.
Monzo says to the central bank, "today I sent RBS £1,500,000", and RBS says to the central bank, "today I sent Monzo £1,200,000". So the central bank just debits Monzo's account with them by £300,000, and credits RBS's account with them by £300,000. The total amount in the central bank remains the same.
So, sure, a bank could claim they sent less money to another bank than they did, but eventually the numbers wouldn't add up, and it would trigger a bucketload of auditing, likely resulting in revocation of banking licenses, and legal issues for both the bank and people involved.
https://en.wikipedia.org/wiki/Net_settlement
There is also a technique involving things called nostro/vostro accounts, where banks have money on deposit with each other, and the sending bank's deposit with the receiving bank is used to cover transfers:
https://en.wikipedia.org/wiki/Nostro_and_vostro_accounts
Of course, then they need to keep their accounts topped up, and they can do that by transfers through other banks, which might be central banks or commercial ones. The nostro/vostro system is suitable for use where banks don't trust each other so much, eg because they are in different countries. I think it was used more in the past, before reliable central settlement schemes were established, but i'm not sure.
You can think of net settlement as being a bit like nostro/vostro where the accounts have infinite free overdraft facilities, and so the banks never build up a credit balance, and just settle their debts at the end of the day.