So the Mantella was designed to be an alternate power source for the Numidium, replacing Lorkhan's Heart. It's not as good as the real deal, but it's good enough that Tiber could use the Numidium to solidify his Empire's dominance, as well as cause Dragon-Breaks like the Middle Dawn and the Miracle of Peace. So I think it's safe to say that the Mantella is still reasonably comparable to Lorkhan's Heart in terms of raw power.

My question is, what effect would the Tools of Kagrenac have had on the Mantella? Could they have been used to attain divinity with the Mantella, much like the Tribunal did with the Heart of Lorkhan? Why didn't the Tribunal create a Mantella for their own use?

I like to think that the idea was something the Tribunal never even contemplated was possible. And yeah, I think that even with their extended world view, they're still quite fallible and not as omniscient as everyone (Vehk) wants everyone believe them to be. Quite frankly, I think they were nice and cozy with the idea of tapping into divinity every once in awhile and just leaving it at that. As far as they knew, the Heart was needed to make the Numidum work, and they didn't want to risk screwing around with their own power source for something that may or may not work. Hence why they gave it to Tiber and Zurin. "As if some humans from some backwater place like Cyrodiil could ever manage to get it working in the fir....aaaaand there it goes crushing Alinor. What the hell."

As for using the Mantella...I suspect it wouldn't be perfect, much like the use of the warped soul gem in Skyrim.

It's my understanding that the Tools of Kagrebac were needed due to the Tonal technology of Kagrenac's enchantment on the Heart.

I'm not familiar with any lore regarding how Arctus fashioned the Mantella. If he had to somehow mirror Kagrenac's enchantment in order for it to work, then the Tools could theoretically be used to manipulate the Mantella in a similar fashion to how they could manipulate the Heart. Anything's possible, I guess, but it's a stretch.

Numidium wasn't used in the Middle Dawn.

The Middle Dawn was caused by the Selectives dancing atop White-Gold.

I like to think that was the moment Sotha Sil just threw his hands in the air and said "I quit!"

Whooops, you're right. I meant to refer to the Siege of Alinor Dragon-Break.

I still wonder how Zurin and Septim figured out how to make the Mantella. Does it perhaps have anything to do with that idea that Zurin is possibly Chevalier Renald?

How to Make a Mantella:

Step One - Obtain Soul Gem

Step Two - Locate Shezarrine

Step Three - Cast Soul Trap on Shezarrine

Step Four - Beat Furiously

Step Five - Mantella

For additional flavor, wait four hundred years and add in one dead Emperor for a delightful Talos cocktail.