This is something I've never considered. I have an account with a high street bank and an online only account. I have never thought about how my relatives might get the money out of my Monzo account (I certainly don't have a Will) if I were to die tragically in the near future (hopefully very unlikely, but...).
Simple - they apply for probate (or letters of administration if you don't leave a will) and your executors/personal representatives send certified copies of the death certificate and probate/LofA to everyone, including banks, life insurance companies, stock brokers, etc., who then release funds to your executors/PR.
The main thing to make sure is that you leave details of ALL your accounts/insurances/investments so that your executor/PR knows where your assets are. In the old days, there'd be correspondence, statements, annual summaries, etc somewhere in your house so your next of kin would be able to search your drawers to see what accounts/assets you had. Now, in this online world, there may be nothing "physical" in your house to tell your next of kin that you have a Monzo account, so they may never know, and your beneficiaries may never get that money - eventually the bank would close the account and put the funds into a "frozen"/suspense account which would languish potentially for decades. Yes, you may have a Monzo card in your wallet, but your wallet may also be lost or damaged in a tragic event that sadly ends your life. That's not unique to a bank that doesn't have local branches - it may apply to any bank or other financial institution which is paperless - even if you did have an online account with a local bank branch, again, if no paperwork in the house and you've not left a note for your next of kin, they may never know about it.
Best thing to do is make sure you write a will and with it, keep a full list of your assets - obviously not security-related issues like account numbers or passwords, but at least a list of bank accounts, insurance policies etc giving name of the financial institution - they can trace your details but your next of kin need to be able to tell them that you have funds with them. Your next of kin or executor can't be contacting every potential financial institution - there are hundreds of them!