A couple of things could be happening here:
Brave is a Chromium based browser - and Chrome browsers changed where and how cookies are stored just before CCleaner v5.88 was released.
It happens now and again, browsers sometimes change things without warning, leaving other apps such as cleaners (and antiviruses) to catch up with what they have changed.
(It happened with Firefox cookies a couple a months ago to make Firefox more secure, Chrome/Chromium just took a couple of months to 'copy' what Firefox did by storing cookies more securely).
This means that CCleaner now needs updating again so that it will clear those new cookie locations for Chromium based browsers, this will happen with the next update, to v5.89, due in a week or two (maybe sooner).
See this for a bit more information:
However you are mentioning more than cookies so there could be another couple of possibilities.
The First is if you have the browser (or extensions/add-ons) set to pre-load or to run in the background after closing.
CCleaner cannot clean a browser if part of it is open in the background, so you have to turn those options off.
The Second, and more likely from what you describe, is 'syncing'.
If you have your browser set to sync then anything that you clean from your machine will be put right back by the syncing.
That's how syncing works, it saves your history, session, cookies, etc. in the cloud and sends it back to all your synced devices that don't have it.
Take a read of the second part of this "Files that re-appear straight after cleaning" for an explanation of why some things that you have cleaned may come straight back, and what you can do to stop some of it happening: