@Venomx I’m not quite sure why you are focusing on a savings account. You would normally receive income into a current account rather than a savings account. So either Monzo, Lloyds, or TSB would be fine for receiving your benefit.
If you do want to have access to a branch account to use alongside your Monzo account (not a bad idea as there are some limitations to Monzo on its own), of your two options I’d be inclined to go with Lloyds, simply because of the IT issues TSB had recently.
However, if you do decide to go with TSB it’s worth pointing out that if you qualify for a Classic Plus Account (one of their current accounts) you can earn 3% interest on money held in that account. To qualify you need at least £500 going into the account every month.
Also, if you have a friend or family member who is a TSB customer, ask them to refer you to TSB. You can both earn £75 if you switch your old Barclay’s or Lloyds account to TSB (I’m assuming you no longer need either of them)
If you don’t know anyone personally who could refer you, feel free to DM me as I could refer you as I have a existing account with them.