O que é um suplemento "oficial" no contexto de D&D 3.5?

There's a formal breakdown

This breakdown is generally considered true across the RPG (and for that matter videogame) community, making for three classes of material:

First Party Material is created and/or published by the developer directly (such as Paizo publishing for Pathfinder or Nintendo making a game for the Wii U). This can be hard copy books (Manual do Jogador), web supplements (such as this Lâmina de guerra release), errata, etc. First-Party material is canonically part of a game, system, and/or campaign setting unless it is overwritten (such as some 3.0 content was overwritten for 3.5) or removed by errata. In your example above, dweomerkeeper is first-party material that has never been removed by WotC (though, please, by all means ban it in your game).

Second-Party Material is made out-of-house but with the developer's permission, approval, and/or involvement. For example, Dragon Magazine is second-party material for the issues of D&D it ran with (in the videogame industry, an example might be how Nintendo contracted another company to create the Metroid Prime games). Second-party material is often considered, rightly or not, to be "less" official and is often perceived (again, rightly or not) as being of lower or inferior quality. Many groups like Pathfinder Society or Living Campaigns do not support second-party material.

Third-Party Material is entirely out-of-house and may or may not have developer approval (even if that approval only takes the form of not issuing a lawsuit). Third party material is completely unofficial and is not supported by organizations such as Pathfinder Society, Living Campaigns, etc, and is often seen as having inferior quality (for an excellent counterexample, see Dreamscarred Press's exciting work with Psionics for Pathfinder). Many DMs/GMs/STs don't approve of third-party material in their own games, though it should be noted that house rules are a form of third-party errata.

A Note About Modules and Campaign Settings

In many cases you'll see adventure modules that have multiple potential outcomes published; these modules can take place inside published settings and sometimes revolve around highly significant events (see Die Vecna ​​Die! as an example). In many cases to find out the 'canonical' ending of a module you'll need to consult a timeline within that campaign setting or even have to read a related novel - or several!

On the definition of "official"

The question posed in the title "What is an “official” supplement in the context of D&D 3.5?" does not have an answer, as far as I can tell. The word "official" is not defined in any D&D supplement to my knowledge.

But there are a few possible interpretations of the word, thanks to Wizards of the Coast's publishing scheme.

The Core Rulebooks

The core rulebooks (the Manual do Jogador, Monster Manual e Guia do Mestre) form the basis of D&D 3.5. This is defined on page 4 of the Dungeon Master's Guide, making it a self-defined system.

The above + content produced by Wizards of the Coast that explicitly declares itself as official

Some content produced by Wizards of the Coast, such as the Errata Files specifically call themselves official.

The above + other content produced by Wizards of the Coast

If we accept that Wizards of the Coast is an authoritative figure on D&D 3.5, its products, when marked with their own logo and published under their name, will be official content.

The above + licensed content by Wizards of the Coast

This is in accordance with a definição do dicionário of the word "official", specifically "appointed or authorized to act in a designated capacity". Notably, this includes Dragon Magazine, when published by Paizo. Observe that at least the Dragon Magazines I have declare themselves as "100% official Dungeons & Dragons® content" on the cover, with no objections that I know of from Wizards of the Coast.

This, including the above categories, is what I consider a reasonable interpretation of the word "official".

The above + other content There is a myriad of material produced using d20/OGL content based on the 3.5 system, such as the Rokugan campaign setting. These are published without Wizards of the Coast's involvement, and do not carry the "Dungeons and Dragons" logo. I can not find a way to define this as official.

On the categories of material you presented

The core rulesbooks

Must be official, as described above.

The main splatbooks and material from setting-specific sources

São indistinguível from a publishing point of view, assuming they come from Wizards of the Coast (note: some aren't affiliated with WotC at all, and would fall into "other content" described above). I can not find a way to call one official and not another - the licensing and legal language found on each one's first page is more or less identical.

Note that not all of these products are necessarily compatível with one another, or meant to be used together in a game. That's a separate issue that does not make any of them a less oficial D&D 3.5 product.

Material from Dragon Magazine

As I outlined above, Paizo had an official licence from WotC to produce Dragon Magazine. It self-declares as Official D&D Content, without complaint by the trademark holder. I find it reasonable to call it oficial. Whether it's a good idea to use it in a game is again a separate issue.

Web supplements

Web supplements are, of course, not conventionally published. I argue that they are still official D&D 3.5 material. First, they are published on Wizard's of the Coast's website, which happens to carry a banner of "Dungeons & Dragons Roleplaying Game Official Home Page", which is a good indicator. Second, and far more importantly, they are marked and published (as they are) with the Wizards of the Coast logo and under their name. Quoting the "More Divinity" web enhancement (the source of the Dweomerkeeper), it refers to itself as "This Wizards of the Coast game product". Despite not being impresso, I find it hard to conclude that these supplements are not "official".

Note that online articles such as Skip Williams' "Rules of the Game" series do não fall under the second condition. Such articles are posted on the official website, but they are not signed and issued by WotC as an entity, just the author of each article.

Old material from 3.0

There is a certain amount of confusion regarding this. All I have been able to find on the interopability of 3.0 and 3.5 is the following clause from the 3.5 Dungeon Master's Guide

This is an upgrade of the d20 System, not a new edition of the game. This revision is compatible with existing products, and these products can be used with the revision with only minor adjustments.

e a online update guide. eu tenho não been able to find a source for the quotation that "anything not updated is automatically valid in 3.5" or similar. I believe it may be an overstated version of the actual DMG text.

The 3.0 products that are referred to are of course published by WotC, but their use in a 3.5 game seems contingent on "minor adjustment" by the DM.

Living Greyhawk

The Living Greyhawk rules do not refer to such general terms as "official products". The last Living Greyhawk Sourcebook released for 3.5 contains an explicit list of sources that are "Open" for use in LG, see Appendix 4. It contains the whole Complete and Races series, and an assortment of other sources, including two Dragon Magazines.

I have seen no official list from WOTC. Their rules questions do, however, seem to give weight in a manner not dissimilar to the following

However, one can take the following hierarchy as typical:

• First Party Materials
  1. Core rulebooks
  2. expansion rulebooks (like DMG II)
  3. splatbooks
  4. setting books
  5. in-house magazine rules articles
  6. in-house magazine non-rules articles

This hierarchy seems to match the priority of the official FAQ except when errata has been applied. Within each step, newer tends to trump older.

They do not ever cite 3rd party materials that I have seen. Were they to add them, however, they would fall into the same pattern, with 7 being licensed versions of all the above.