Yes, they do
You posit:
If a lvl 20 Wizard used the Shapechange spell to become an Ancient Brass Dragon, then they retain all their Wizard class features.
Minor quibble with the phrase "to become an Ancient Brass Dragon". Shapechange doesn't let you "become" a dragon (as opposed to True Polymorph, which does). Rather, Shapechange lets you "assume the form" of a dragon, which in this case is actually important, because while shapechanged, and unlike while polymorphed:
You retain the benefit of any features from your class, race, or other source and can use them, provided that your new form is physically capable of doing so.
So now you are still a 20th level wizard (but a shapechanged one), with all the class features that implies, and the only restriction being that to use those class features the dragon form must be physically capable of doing so.
At the same time you are a wizard:
Your game statistics are replaced by the statistics of the chosen creature
This means you can in fact use the Change Shape feature of the Ancient Brass Dragon, since that feature is part of its stat block. When you use the Change Shape, you can, as an action, polymorph:
into a humanoid or beast
which lets you return to whatever your wizard race was (or any other humanoid race, for that matter). Note that you are polymorphing into a "humanoid" and not a 'wizard'. However, for your dragon form, your:
statistics and capabilities are otherwise[1] replaced by those of the new form, except any class features or legendary actions of that form. (emphasis mine)
That is to say, your current statistics and capabilities are replaced by those of the (generic, classless) humanoid except for the humanoid's class features. If the new humanoid form's class features do not replace yours, then your class features are retained. And since your class features are currently those of a 20th level wizard, you get to keep those.
Thus - at least until the duration of your shapechange expires - you have the changed shape form of a humanoid with the class features of a 20th level wizard.
1The use of "otherwise" here refers to the fact that you do retain the "statistics and capabilities" of the dragon form enumerated in the previous but unquoted sentence. That is, after you change shape, regardless of your new shape, you keep the dragon form's "alignment, hit points, Hit Dice, ability to speak, proficiencies, Legendary Resistance, lair actions, and Intelligence, Wisdom, and Charisma scores, as well as [the change shape feature]"