Is dropshipping saturated?
The obvious products are, and that is a different statement. What is saturated is selling the same catalogue everyone else has to the same audience through the same ads.
In more detail
What is not crowded is anything requiring local knowledge: a category with real service attached, a market whose delivery and payment habits outsiders get wrong, an audience somebody already belongs to. Those are harder to copy than a product page.
What to do about it
The margin is thin by design, so the whole model depends on cheap traffic. When advertising gets more expensive, dropshipping stops working before anything else does.
A dropshipper who survives past the first year almost always stops dropshipping — they start holding stock for their best sellers, because that is where the margin is.
Returns are where the model is tested. If your supplier will not take a return, you are the returns department.
The mobile app angle
An app is worth building once people buy from you a second time. Most dropshipping stores never reach that point, which is why the honest answer here is usually ‘not yet’.