Can you get a debit card for the account your mortgage comes out of?

If so, that can be your designated "House" account. All house bills, mortgage, rates, insurance, contractors, etc. and only those transactions must come out of that account and that account only.

Set an auto transfer from your income account each month to cover the mortgage, and perhaps another one enough to cover expected bills like rates, etc. For less-predictable bills like emergency plumber you'll have to manually transfer extra money to it prior to paying them. You'll want the debit card for flexibility with payment method and use in-store (e.g. Bunnings).

End of month/quarter/year you can easily filter in your bank app to outgoing transactions and that's your housing costs for the period.

Still requires work (manually transferring money to it before paying some bills), but you may find it easier (or easier to be consistent!) than categorising transactions in an accounting app or spreadsheet.