if anyone feels there is room for improvement in my post, I welcome Edit suggestions over downvotes. thank you in advance for all of your assistance and advice.

It's not clear what you mean by "What is the official damage dice progression?". What do you mean by "progression"? Weapon damage doesn't change as you level up (other than ASIs increasing the relevant ability score, and potentially getting magical weapons).

@V2Blast It's a term that players of certain previous editions will recognise. We can leave it to those who are expert in both D&D 5e and the concept of damage-dice progression to tackle the question.

Found corresponding questions for Pathfinder (Pathfinder Damage Dice Steps) and Starfinder (What is the damage progression?), in case anyone finds those useful to reference.

Indeed, it is also used in 5e when talking about what is known as "Leveled Cantrips", for example the Cantrip Fire Bolt uses the Cantrip Dice Progression, whereas Eldritch Blast uses the Cantrip Beam Progression. Also I already further elaborated on my definition with an explicit example of a PC commissioning an NPC to craft a custom Weapon. Not sure why the Tags were removed as they are indeed pertinent to the Question. I'm even including an explicit Crafting example, and Weapon Size is one of the Facets directly related to Weapon Damage.

additionally: The System used was in the Title to improve external Search Results, that was intentionally included to direct more people to here and less people to repeating this query. As I'd stated, I have searched for this content for Days. as for the Tags: "questions about adjusting adventures depending on the number of players or other factors." This falls under other factors for potentially multiple PCs, & "Errata is corrected material that came out after a book has been published and circulated" such as the WotC Twitter feeds everyone loves to reference, which is official Errata.

A comprehensive list of all damage dice progressions strikes me as too broad. For instance, every other class and subclass has some kind of unique dice progression. Many if not most spell have dice progression too, are you expecting a list of all such spells?

The Spells either fall under the "it states it's damage" rule, or Cantrip Dice or Cantrip Beam progression. a simple list of Books & Pages to reference would work just fine as well, the primary problem is there is no specific mention of where to look comprehensively. Most Classes have specific abilities, but not as many actually use Damage Dice Progression as far as I am capable of seeing. Monk does (Unarmed Strike), Rogue does (Sneak Attack), Bard however doesn't deal Damage with his Bardic Inspiration, thus, excluded.

When you assume the answer in the asking of a question, it makes the question a little unwieldy.

Almost everthing falls under "it states its damage" rules, I do not see how spells are different in that regard. Moreover, if cantrip beam progression is applicable, are features like extra attack applicable too? And I think you are underestimating how case-by-case the class features are, for instance bardic inspiration is damage dice progression for at least one bardic college. Well, either way, I might give it a shot tommorrow.

Tags aren’t merely for examples used by a question to help explain it. We use tags only to categorise questions by problem subject. Unless this question is explicitly and only about crafting oversized weapons (in which case, the txt is missing relevant parts and requires editing), the tags don’t belong. As for [scaling], that’s not what it’s for at all.

I might be underestimating it, but I have limited it to Damage Dice, which cuts out a large amount of Classes and Class related abilities. Without a comprehensive list, how can I gauge how far I underestimated it by? I honestly lost count of how many days I've spent googling this, it's over 120 Hours (5 Days). (Yes, English is weird, and confusing, and migraine inducing)

The player Requests a Light+Finesse Greatsword using Mithral Metal; What's the Damage? I have no Idea. The Player Requests a Heavy+2-Handed Steel Chain Whip; What's the Damage? I have no Idea. I only have Monsters available to me for examples, and even that is not actually talked about beyond "Natural Weapons" as far as I am aware. What if I want to give a Storm Giant dual Great-Axes, what's the Light limitation? these are covered in my question. The Player is requesting a custom piece of Equipment; All of the previous examples are on that list, as it is in fact custom.

because that is a separate problem

I don't know what is unclear about it other than the fact that you all keep changing the prime directive of my question.

After reviewing the recent changes to this question, it is unworkable if it keeps changing. It is currently locked to end the constant changing. Please, post your other question about crafting separately from this question about finding the official damage dice progression. By site policy, we cannot have a question post contain two questions.

@BlueShocker64 is there an example of a similar compilation from another game system you could link to? I think I need to see the form of an acceptable answer before trying to create one for 5e

2nd result of "d&d size chart 5e" has this 3.5 result: dandwiki.com/wiki/SRD:Table_of_Creature_Size_and_Scale Of course, this chart is entirely incompatible, because that is a Creature Stat modification chart based on size, which is a feature that 5e does not rely upon, but 3.5 does. another example would be the multitude of Leveling Tables in 5e for the various Classes and Archetypes. Cantrips are another example as they follow a simple algorithm of (Calc.exe equation): (Int((Level +1) /6) +1) (Int(): always Round Down rule, Level: Player Level).

I made an edit to bring the question in line with your comments from today. Is this still what you are asking?

@DavidCoffron NOPE! not even close!