Related--
and
In the US, how does the distinction between E2 and E3/E4 airspace affect pilots?
In short, the situation is ambiguous as to whether ultralights may fly in the "extensions" without "prior authorization".
What is not ambiguous, however, is that if we answer "no", then we must recognize that the airspace we are talking about extends upwards indefinitely, due to the "within the lateral boundaries of" language used in the regulation. The same is true of E2 "surface area" airspace (example KONP), which is not an "extension" and which is unambiguously within the scope of the airspace addressed by the regulation (103.17) and therefore off-limits (without prior authorization) for ultralight flight.
The idea that the off-limits airspace somehow has a cap at 700' AGL or 1200' AGL, or in the case of an "extension", at the ceiling of the adjoined Class D airspace, is not supportable at all.
The truth is that the FAA is deeply divided as to whether phrases in the FARs like "surface area", "designated for an airport", and "surface area of controlled airspace designated for an airport" should or should not be construed to include surface-level Class E "extensions".1 Ambiguity around this issue has existed ever since the 1993 "alphabet" airspace re-designation.2 There's some consideration of a future rule-making effort to address this issue.3 It's possible that the language in AIM 3-2-6, as well as in the legend of the Chart Supplements, that reads "Surface area arrival extensions become part of the surface area and are in effect during the same times as the surface area" will be changed in the future to avoid implying that all regulations that apply to the core "surface area" should automatically be construed to apply to the surface-level Class E "extensions" as well.4
Footnotes:
1,2,3,4) Source-- comments made by high-level FAA staffers during April 2021 airspace charting meeting.