I am running Brave 1.6.4 in iOS12 on an iPad Air 2 although the behaviour was also evident under iOS11.
Essentially when Brave is running in the background, even with no tabs open, swiping between home screens on my iPad becomes slow and jerky. Quitting Brave solves the problem.
My set up is private tabs by default and all individual controls except ‘Block Scripts’ enabled. I have 1Password 7.2 as the selected password manager.
When updating to iOS12 this week I did a clean install from DFU mode, and didn’t restore any content from backup.