You really should disable this extension, at least as a debugging step. Chromium browsers already have a tab suspension system built in called discarding which you can view at brave://discards (or in Chrome, chrome://discards). I don’t know about the extension in question - but there have been clear cases of malware, like with The Great Suspender.
If you don’t want to turn the extension off, there’s a way you can check the usage (CPU and memory). In Brave go up to the Hamburger menu (three lines, top right), pick More tools from the menu and then the sub-item Task manager.
With that open, you’ll want to look for Extension: Tab Suspender in there and watch what its usage is. You can right click in the middle of the task manager which will bring up a context menu with options… tick the box for Profile so you can get a breakdown. The Task manager will show which processes in Brave are running under which profile