What is the most mana that can be produced by tapping a single permanent in future standard?
At least 3^(2^^^^39)

Decklist:


4x Nyxbloom Ancient
2x Thousand-Year Storm
1x Repeated Reverberation
1x Narset&#39;s Reversal
1x Quasiduplicate
1x Dance of the Manse
1x Wilderness Reclamation
1x Teferi, Time Raveler
1x Awakening of Vitu-Ghazi
4x Izzet Guildgate
4x Simic Guildgate
4x Boros Guildgate
4x Swiftwater Cliffs
4x Temple of Epiphany
4x Azorius Guildgate
3x Gruul Guildgate


Setup for combo

The setup involves the following:


Drawing cards until we have Wilderness Reclamation and 7 other cards in hand, and discarding Wilderness Reclamation to hand size.
Drawing cards and playing lands until we have drawn and played 4 Izzet Guildgate, 3 Simic Guildgate, and 1 Boros Guildgate and all other non-land permanent cards, and drawn all of the instants and sorceries.
Casting Dance of the Manse with X=6 targeting Wilderness Reclamation to put it onto the battlefield as a 4/4 creature.
Casting Awakening of Vitu-Ghazi targeting a 


This takes 14 turns to draw all of those cards, and we can finish playing them earlier than that.

Combo

We have no way to untap lands, so we can construct a "loop" that is ultimately limited by the mana that can be generated by the lands on the battlefield.

A loop iteration is as follows:


Cast Repeated Reverberation. Allow all Thousand-Year Storm triggers, previous Repeated Reverberation triggers, and copies to resolve, but leave the original spell on the stack. This copies the next spell to be cast a number of times equal to 2 * (2 * storm count + previous RR triggers). This costs {2}{R}{R}.
Cast Narset's Reversal targeting the Repeated Reverberation card. By now, the storm count is at least 1, so both of the Thousand-Year Storm triggers make at least 2 total copies of Narset's Reversal. Have 1 copy target the Repeated Reverberations card, and the other target the original Narset's Reversal card. The result is that we get 1 more copy of Repeated Reverberation, and all cards on the stack return to the hand. This costs {U}{U}.
Allow all of the copies of Repeated Reverberation to resolve.


This loop iteration costs 6 mana in some combination of {U} and {R}, increases the storm count by 2, and makes twices as many of the next spell to be cast. For the loop, we tap a land for {U} and a land for {R} (both modified by Nyxbloom Ancients), and repeat this loop until we have 5 mana remaining. We spend that 5 mana to cast Quasiduplicate targeting Nyxbloom Ancient, allow all of the copies to resolve, and cast Narset's Reversal to return both cards to the hand. Then we tap another two lands for much more mana, and repeat the process.

When performing this loop on a full set of untapped lands, when spending the last mana on Quasiduplicate, target the awakened Izzet Guildgate instead of Nyxbloom Ancient. When performing the loop during the main phase, target the animated Wilderness Reclamation instead

Then, in a full turn, we do the following:


Activate Teferi's first loyalty ability so that we can cast sorcery spells at instant speed.
Perform the loop described above, copying Nyxbloom Ancient, and with the last lands, Wilderness Reclamation
For each Wilderness Reclamation trigger, perform the same loop, copying Nyxbloom Ancient, and with the last lands, Izzet Guildgate


In the long run, the doubling from Repeated Reverberation far outpaces the storm copies from Thousand-Year Storm, so we can approximately say that each loop iteration doubles the number of copies 8 times. So, after we tap a pair of lands for M =  2 * 3^N mana, where N is the number of copies of Nyxbloom Ancient on the battlefield, we can make approximately 2^((M-5)/6) copies of Nyxbloom Ancient. In the longer run, the multiplicative factors don't even matter that much, so we can say that the number of Nyxbloom Ancients we get from tapping one land is about 2^(3^N), where N is the number we previously had.

2^(3^N) is much greater than 2^(2^N), so we can say that every time we untap our lands, we get more than 2^...^K Nyxbloom Ancients and Izzet Guildgates or Wilderness Reclamations, where K is the number of Nyxbloom Ancients we untapped with and the number of 2s is equal to the number of Izzet Guildgates we untapped with. In Knuth's up-arrow notation, this is much greater than 2^^N, where N is the number of Izzet Guildgates. So, each turn we get 2^^N Wilderness Reclamations and repeat that process in response to each Wilderness Reclamation trigger. That gives us 2^^^(2^^N) Izzet Guildgates.

We repeat that process for the 39 turns it takes to draw the rest of the library, getting more than 2^^^^39 Guildgates, Nyxbloom Ancients, and Wilderness Reclamations. In the end, we tap the last land for more than 3^(2^^^^39) mana.



This cannot go infinite because every land in the decklist unconditionally enters the battlefield tapped, and we can only untap lands during the untap step and a bounded number of times each end step because of Wilderness Reclamation. So, creating more lands can only increase the amount of mana available the next time we untap lands, and the number of times we can untap lands each turn is bounded.



Credit to Arcanist Lupus's answer for the idea of using Wilderness Reclamation, and using Dance of the Manse to be able to copy it with Quasiduplicate.