Using System Preferences doesn’t usually allow you to remap keyboard shortcuts in apps — only to assign the new ones. If the keyboard shortcut already exists for another action, it’s likely it will remain so even if you set the shortcut via System Preferences (for any app, not just Figma). To remap shortcuts, I would suggest using Better Touch Tool (I use it daily) or Maestro Keyboard. They are both reliable apps that allow you to do even more than simple shortcut remapping.
Have you tried to re-map keyboard shortcuts in OSX recently? Have been able to map existing shortcuts and override them in Spotify and Chrome with no issue.
Also, mapping with another keyboard shortcut makes the Figma shortcut work as anticipated, it seems to be that Figma somehow overrides the Shift Command [ and Shift Command ] shortcuts.
Just tried to assign the New Tab shortcut in Chrome (Cmd + T) to “Extensions” menu action. It didn’t work until I also assigned a new shortcut to the “New Tab” action. Since in Figma the next tab/previous tab don’t even have this shortcut in the menu (they use Ctrl + Tab/Ctrl + Shift + Tab), I guess these alternative shortcuts are indeed set somewhere deeper.