Yes you can true polymorph into an ancient brass dragon

As you say, the spell and rules are clear. An ancient brass dragon is a creature, it is not a shapechanger (and may not matter if they were), and it is of the appropriate CR for your level.

Thus, there is no reason why you would not be able to use true polymorph in this way.

Ancient Brass Dragons are not shapechangers

Ancient Brass Dragons are not considered shapechangers. A creature is a shapechanger if they have the monster subtype (Shapechanger). Ancient Brass Dragon's creature type is dragon.

The fact that it is able to change shape (a special ability) is irrelevant to being able to transform into that shape. The dragon does not have the shapechanger subtype, thus it won't be potentially conflicted with the shapechanger subtype restriction.

You can use all the abilities of your True Polymorph form

The target’s game statistics, including mental ability scores, are replaced by the statistics of the new form.

Jeremy Crawford says:

When a game effect, like Wild Shape, says you use a creature's statistics, you use its stat block (see "Statistics," MM, 6).

According to that same section "Special Traits, Actions, and Reactions" are part of a monster's stat block.

Ability to change shape back to your old form is unclear.

It is worth noting that you may not be able to use change shape to change back into your old form: Can you use a Dragon's Change Shape Ability to Turn Back Into Yourself?

What are proficiencies?

The dragon retains its proficiencies, but what counts as a proficiency? In the Character Creation chapter, a character's proficiencies are defined as follows:

You also gain a number of proficiencies: armor, weapons, skills, saving throws, and sometimes tools.

The term is bolded in the original text, as this is the place where it is first defined. A couple sections later, the concept of a proficiency bonus is introduced (emphasis mine):

Your proficiency bonus applies to [...]:

• Attack rolls using weapons you're proficient with
• Attack rolls with spells you cast
• [...]

Your class determines your weapon proficiencies, your saving throw proficiencies, and some of your skill and tool proficiencies. [...] Be sure to note all of these proficiencies, as well as your proficiency bonus, on your character sheet.

Proficiency bonus is not mentioned in the list of proficiencies above, and it is noted separately from the proficiencies themselves. Therefore, a character's proficiencies indicate instances where the proficiency bonus is added, but the bonus itself does not count as one of the character's proficiencies. When a character reaches level 5, their proficiencies (usually) do not change; instead, their proficiency bonus increases to +3.

Does this apply to monsters?

While monsters have many abilities unavailable to PCs, they are typically built using the same set of rules. The introduction to the monster rules refers back to the player rules in the sections for Size, Alignment, Hit Points, Speed, Ability Scores, etc. What about saving throws and skills? Are monsters proficient in them?

The Skills section comes right out and says it (emphasis mine):

The Skills entry is reserved for monsters that are proficient in one or more skills. [...]

A skill bonus is the sum of a monster's relevant ability modifier and its proficiency bonus [...]

The Saving Throws section almost says the same thing:

The Saving Throws entry is reserved for creatures that are adept at resisting certain kinds of effects. [...]

A saving throw bonus is the sum of a monster's relevant ability modifier and its proficiency bonus [...]

To me, the intent is clear: monster saving throw bonuses also count as proficiencies, much like a PC's class saving throw bonuses do.

Comparison

When using Change Shape, an Adult Gold Dragon retains its proficiencies. I will compare its saving throw and skill bonuses in dragon form to those in Archmage form.

Adult Gold Dragon

The dragon's proficiency bonus is +6, because it is a CR 17 creature. Creatures of CR 1-20 have the same proficiency bonus as PCs of the same level.

• DEX +8. The dragon's Dexterity (+2) plus the dragon's proficiency bonus (+6).
• CON +13. The dragon's Constitution (+7) plus the dragon's proficiency bonus (+6).
• WIS +8. The dragon's Wisdom (+2) plus the dragon's proficiency bonus (+6).
• CHA +13. The dragon's Charisma (+7) plus the dragon's proficiency bonus (+6).
• Insight +8. The dragon's Wisdom (+2) plus the dragon's proficiency bonus (+6).
• Perception +14. The dragon's Wisdom (+2) plus double the dragon's proficiency bonus (+12).
• Persuasion +13. The dragon's Charisma (+7) plus the dragon's proficiency bonus (+6).
• Stealth +8. The dragon's Dexterity (+2) plus the dragon's proficiency bonus (+6).

Of particular note is the dragon's Perception bonus. Much like a rogue with Expertise, the dragon adds double its proficiency bonus to Perception checks. The Skills section tells us about this possibility:

For instance, a monster might have a larger-than-expected bonus (usually double its proficiency bonus) to account for its heightened expertise.

Adult Gold Dragon → Archmage

The Archmage's proficiency bonus is +4, because it is a CR 12 creature. When an Adult Gold Dragon uses Change Shape to become an Archmage, its saving throw and skill bonuses are as follows:

• DEX +6. The Archmage's Dexterity (+2) plus the Archmage's proficiency bonus (+4).
• CON +5. The Archmage's Constitution (+1) plus the Archmage's proficiency bonus (+4).
• WIS +6. The dragon's Wisdom (+2) plus the Archmage's proficiency bonus (+4).
• CHA +13. The dragon's Charisma (+7) plus the Archmage's proficiency bonus (+4).
• Insight +6. The dragon's Wisdom (+2) plus the Archmage's proficiency bonus (+4).
• Perception +10. The dragon's Wisdom (+2) plus double the Archmage's proficiency bonus (+8).
• Persuasion +11. The dragon's Charisma (+7) plus the Archmage's proficiency bonus (+4).
• Stealth +6. The Archmage's Dexterity (+2) plus the Archmage's proficiency bonus (+4).

In general, during Change Shape a dragon's saving throws and skills are weakened; however, there are exceptions. A Githzerai Anarch (MTF, p. 207) is a CR 16 creature (+5 proficiency bonus) with 21 Dexterity (+5), raising the dragon's Dexterity save bonus to +10.

Rules-as-written, the decision of whether a proficiency bonus should be omitted, included, or doubled is maintained, while the proficiency bonus itself changes to match the creature changed into.