I’m not an expert on this but I think you need to think about what situations your parents will face in the future and which arrangements will suit them best. It also depends how much money we are talking about. My DH and SIL did this for his parents when his mums Parkinson’s was advancing and it sparked all kinds of bigger financial discussions.
Eg if your father goes into residential care, then his income (pensions) and savings (half of any joint accounts) will be taken to pay for it. How much income does your mum have on her own? Could she live in her own pension or will she need to apply to keep some of his?
How do they own their property? Joint or in common?
first step was simply to sit down with the paperwork and make a list of all the accounts, what type they were, and what was happening with each / what it’s used for. Also all investments, and other assets eg car etc. Importantly you need to know whose name they are in.
Then a review of all the direct debits going out / money coming in their main accounts. DH found that his dad had two expensive subscriptions for broadband/internet running concurrently, that he was paying charges on multiple store cards he didn’t know they had (MIL had taken them out before she got ill), and that they had taken out a pointless large loan secured on the house at a swingeing interest rate and paying huge charges for nothing. It was ‘just in case’ - FIL liked seeing a big sum sitting in his current account.
We also found out after MIL died that she was actually the registered owner of their car, not FIL. she’d been in a home for years by that point and not driving anywhere.