That’s how Chromium cache works, you either accept that fact, use InPrivate Window or use Safari.
Brave is Chromium and Safari is not Chromium so it doesn’t make sense to compare each other when they are totally different, Blink stopped being a Webkit fork long time ago.
You deleting the files doesn’t really do much but forcing the browser re-download whatever files it is writing, which means you are unnecessarily wasting your disk lifespan because Brave/Chromium in normal window, will keep adding Cache files when you browse the web.
Brave recently added back a way to see cookies and other storages form websites, use it brave://settings/content/all just clean the ones that make sense.