Will a takeaway iced-coffee cup fit?
Check the bottom rather than the lid diameter.

Measure where the fins hold
Measure the outside diameter of the lower cup: 2–3.15 inches inclusive. A wide lid does not describe the base.
Look at the cup shape
A tapered or flexible cup needs a full seating check. Do not force a cup into place based only on its advertised volume.
Keep the lid question separate
A fitted lid can still have an open straw hole. Steadi does not close that opening or prevent liquid escaping through it.