Dragon Forms & a Little Bit of Wyrmling Pediatrics
I imagine that dragons have 3 forms. Their natural, full dragon state (4-legged in the case of elder dragons), a small, human-like form, & a sort of in-between form. The largest being their dragonus form.
Make no mistake, a dragon can never truly look human unless they are skilled enough in dracomancy, as to become a true human facsimile is something that doesn't come naturally for a dragon.
Even the small form they take is basically them as a human-shaped & sized dragon. In this form, they have no muzzle, instead bearing a humanoid face, however, beyond that, they are draconic. They have the scales, the wings, the tail, the horns, the claws, the talons, the fangs, everything. This is their draconian form.
On the other hand, the in-between form is twice as big as the small one & despite having a humanoid bodyshape, they bear a more dragon-like visage than the draconian form, just on 2 legs. Especially in their head shape. This form has many of the benifits of the other 2, if to a lesser extent. A similar maneuverability to their small form, but a strength more in line with their large form. They also frequently switch between walking on 2 legs & 4 very often. This is their dracolithe form.
As mentioned before, each form has it's advantages & disadvantages. The dragonus being power, draconian being enhanced swiftness, flexibility, & maneuverability, & the dracolithe being a mix of both, but again, to a lesser degree.
Of course, every type of dragon has their own features. Such as wyverns & longs. So their appearances when in these forms do reflect what they are. Arm wings & 2 legs for wyverns & deer-like horns, no wings, a strip of hair down the spine, & sometimes whiskers if they're longs or ryus.
On the other hand, most draconids (half dragons) can't take full-dragon form unless they're descended from an elder dragon &, even then, they can't do so until they reach the age where dragons are fully mature.
So, like, 100 years of age. (Citation needed.)
They are in a midway point between draconian & human form at birth (or hatch depending on your hc) & do have access to a purely human & purely draconian form upon taking their first breath even if it takes time & practice to do so, but they need to reach dragon teen years before they can take on dracolithe form.
(Worldbuilding/Note: Not being able to take on either full human or full draconian form by age 3 usually indicates a bit of a developmental issue, but it's normally nothing that could harm the wyrmling medically & just means that it could take them longer to do so. Parents should also note that the difficulty is not a direct symptom of a developmental problem, but rather a side-effect of one & said problem won't stop the wyrmling from being able to eventually take on the problem form unless there is a severe imbalance between human & dragon dna which could actually lead to real medical issues, so pediatric shaman dragons suggest that it's best to keep an eye out just in case. However, consistent difficulty with transforming into both at age 3 is a much higher possible indication that the child has some sort of medical problem & should definitely be monitored.)
Again, draconids naturally take on a draconian-human mix form as that is their default, though they are also able to take on both full-human & full-draconian form right off the bat with enough practice & with enough experience, both draconian & human forms will become like second nature to them. However, it takes increasingly more work & practice to take on dracolithe & dragonus forms.
The aging only gives them access to these forms, not automatically allow them to become them whenever.
While draconids don't naturally have quite as close of a connection to the elements as their draconic parent, supplementing that with their element's mantic parallel can alleviate quite a bit of that. It just takes more work.
Another benefit to being draconid is the access to human-specific magic which has it's own benefits as humans are industrious by nature & so their magical abilities reflect this.