Ctrl + Tab and Ctrl + Shift + Tab
I'm using Vivaldi from 5 minutes and I saw that shortcuts Ctrl + Tab and Ctrl + Shift + Tab works in works in another way than in for instance Firefox, Chrome. I think that it's common shortcut and it should work like in others web browsers.
I was struggling with the issue as well. Go to Settings > Tabs (instead of keyboard) > TAB FEATURES > Cycle in Tab Order