Wero seems promising. But I am confused as it appears they have acess to my bank account's balance and transaction history. The privacy policy (Archive.org) states on page 4

Purpose: Displaying your account information (performance of a contract – art. 6.1.b of GDPR)

Categories of data processed: Balance and transaction history of your payment account

Retention period: Duration of the contract (the Wero General Terms & Conditions)

The term "payment account" is not properly defined in the document, but I would infer from the first line on page 4 that it is the connected bank account.

This would be significantly more invasive than PayPal. Would be a dealbreaker for me, as I don't even see a plausible reason for doing this.

Their FAQ states the contrary:

Wero does not have access to your transactions or any other account activity beyond the information we need to complete a Wero payment.

Again, "information we need" is quite vague...

Update: Wero confirmed

See my comment below, Wero's Data Processing Offices confirmed via email that they do access your bank's transaction history, depending on which implementation mode your bank chose.

Quite invasive, IMHO