That is only dealing with a business. Private can pay cash whatever they want.When you do transfers online using companies like CurrencyFair, there is a drop-down list where you have to indicate the purpose (e.g. to transfer salaries or pensions, or to purchase property). There is no maximum limit to the amount you can transfer.
I think a €2000 limit for cash transactions was brought in last year to try and cut down on tax evasion etc. but I don't know how strictly it is enforced. That wouldn't apply to bank deposits anyway.