That would be the optimization progress bar! It represents your progress towards the next sector optimization. You can view the specific number of upgrades still needed in the tooltip for the sector by hovering over its center button or upgrade button. Optimizations double the processing speed of the sector.
There is not an ever-present location to repeatedly click for some benefit. As you noted, the only place and time which clicking as fast as you can benefits you is on a sector while it is having a breakthrough. I hope this helps!
It would be helpful if there was an auto attack option for our pet. Maybe a skill tree that would have him click so many times based on how many skill points you put in it.. or give him extra abilities/multi hit etc... get tired of clicking and not a big user of auto clickers. thanks.
Thanks for the suggestion! We'll note this down. We have a planned progression system for Feli. For now, we only have the core gameplay and we'll slowly add new features/progression system as we go. Stay tuned :)
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 "Re:Archer"){kind=icon}
 "Immortal Hero Idle"){kind=icon}
 "Monster Clearer"){kind=icon}
That would be the optimization progress bar! It represents your progress towards the next sector optimization. You can view the specific number of upgrades still needed in the tooltip for the sector by hovering over its center button or upgrade button. Optimizations double the processing speed of the sector.