Can QBO generate report found easy in Quicken: a report listing account transactions according to category, where all transactions grouped together per category?

I'll share a report that you can use, bwccacct.

While we're unable to get a specific report for the account category, you'll want to run the Transaction Detail by Account. This report will display the transactions and total for each account in your chart of accounts.

To run the report, here's how:

1. On the left panel, select Reports.
2. Type Transaction Detail by Account in the search field.
3. Set the Report period and click the Customize button.
4. Go to the Filter section and select the transaction type you'd like to view from the Transaction Type drop-down.
5. In the Account drop-down, mark the accounts you'd like to view in the report.
6. Hit the Run report button.

Here's also an article for reference: Customize reports in QuickBooks Online.

To check the other reports in QuickBooks Online, you can click on this link:Reports included in your QuickBooks Online subscription.

For any follow-up questions about the reports, please let me know in the comments below. I'll be around to answer them. Take care and stay safe.