The short answer: "it depends". The FAA does not take a consistent approach to this question.
On the one hand:
In April 2022, SIT/PASI at Sitka Alaska featured a large E4 surface-level Class E "extension" extending 28 miles northwest of the airport, adjoining a core E2 surface-level Class E airspace area that surrounds the airport out to a radius of 4.2 nm and also has a small projection to the southwest.1,2 Why the airspace was designated this way, rather than simply all designated as part of a single E2 surface-level Class E airspace area, is unknown to this answerer and is the subject of a related ASE question. At any rate, the surface-level controlled airspace northwest of SIT/PASI beyond 4.1 nm from the airport was an E4 surface-level Class E "extension", exactly as is the airspace at KSTS referenced in the present question. Note that at SIT/PASI, the boundary between the core E2 surface-level Class E airspace and the large E4 surface-level Class E "extension" was not shown in any way on the sectional chart, exactly as is still the case for KACV, KSGU, and KBIH.3
While this airspace configuration was in effect, I spoke to a staffer at the FSS at Sitka Alaska, which was responsible for actually issuing SVFR clearances for the airspace near SIT/PASI, and was informed that 1) a Special VFR clearance would be valid throughout the entire surface-level Class E airspace, including the E4 "extension", and 2) the E4 "extension" was having a negative impact on Coast Guard helicopter training operations because when the ceiling is lower than 1000' AGL in that area they couldn't operate VFR there without a Special VFR clearance, and since SVFR clearances are issued on a one-in one-out basis, that was not compatible with extended training operations.
So at this particular airport, the folks involved in actually issuing a SVFR clearance did consider it to be valid for the entire surface-level Class E airspace including the E4 "extension" extending 28 miles to the northwest, and also did consider FAR 91.155(c), the prohibition on VFR operations below a ceiling lower than 1000' AGL without a Special VFR clearance, to cover the entire surface-level Class E airspace, including the E4 "extension" extending 28 miles to the northwest.
Incidentally, the FSS staffer I spoke to used the term "surface area" to refer to the entire surface-level Class E airspace in this area, including the E4 "extension" extending 28 miles to the northwest.
And on the other hand:
FOR AN OPPOSING VIEW, SEE THIS DOCUMENT, which states that 91.115c does NOT apply to surface-level Class E "extensions" (E3/E4 airspace), and also states that SVFR is NOT permitted in surface-level Class E "extensions":
Obviously, this memorandum begs the question of why, if the distinction between the core E2 surface-level Class E airspace and the E4 surface-level Class E "extension/s" has such regulatory significance, the boundary between these two airspaces was not indicated on the sectional chart at SIT/PASI circa April 2022, just as is still the case at KACV, KSGU, and KBIH.
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".4
Ambiguity around this issue has existed ever since the 1993 "alphabet" airspace re-designation.5 Various FAA issuances in the past have given conflicting answers to this question.6 Pilots have failed check rides due to the confusion and ambiguity around this issue within the Agency.7 There's recently been some consideration of a future rule-making effort to address this issue.8 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.9
Perusing the related links below will reinforce the idea that "your mileage may vary".
Some of the answers to the ASE questions linked below--particularly the last two questions in the list -- delve into the specifics of the phraseology in various FARs and in the "Airspace Designations and Reporting Points" document, and explore why it is arguably unclear as to whether phrases like "within the lateral boundaries of controlled airspace designated to the surface for an airport" (the specific phrase used in FAR 91.155(c)), "within the lateral boundaries of the surface area of Class E airspace designated for an airport", and other similar phrases should or should not be construed to include surface-level Class E "extensions" (E3/E4 airspaces). The last link explores in detail how an apparent bureaucratic accident or oversight, not directly supported by any specific rule-making action, "muddied the waters" and obscured the FAA's original intent for the surface-level Class E "extensions", which was that they be governed by the same regulations as apply to other surface-level Class E airspace.
Clearly, the most conservative and safest course of action for pilots is to assume that--unless specifically advised otherwise by local ATC-- FAR 91.155(c) should be considered to apply to E4 surface-level Class E "extensions", not just to the core "surface areas" that actually surround the airports for which they are designated--regardless of whether or not the controlling agency in any given instance is actually willing to issue a SVFR clearance for flight within the E4 "extensions". Also, whenever a pilot is issued a SVFR clearance for a given controlled airspace, he or she should verify whether or not the controlling agency intends that SVFR clearance to include any adjoining "extensions", in any case where that might be a factor.10
Footnotes:
In April 2022, the E4 surface-level Class E "extension" at SIT/PASI (Sitka, Alaska) was 12 miles wide, and extended to 28.3 miles northwest of the airport. For the E-4 airspace description, see page E-158 of the "Airspace Designations and Reporting document FAA Order 7400.11F. The E-2 airspace description appears on page E-9. Both of these airspace descriptions were modified on 11-05-2020, which is when the large E4 "extension" was introduced.
The airspace configuration at SIT/PASI was changed effective 7/14/22-- see https://www.federalregister.gov/documents/2022/06/01/2022-11591/modification-of-class-e-airspace-and-revocation-of-class-e-airspace-sitka-rocky-gutierrez-airport-ak. There is no longer any E4 "extension" at SIT/PASI.
Re KACV, KSGU, and KBIH: see related ASE question What is the primary reason that the non-towered airports ACV, TVL, SGU, BIH, and SIT/PASI have E4 extensions to E2 airspace?
4,5,7,8,9,10. Source-- comments made by high-level FAA staffers from Airspace and Flight Standards divisions, during April 2021 Aeronautical Charting Group meeting, discussion of item 21-01-360 (minutes are given at https://www.faa.gov/air_traffic/flight_info/aeronav/acf/media/minutes/ACM_21-01_Minutes.pdf, but do not reflect these particular details.)
- See related ASE answer What indication has the FAA given that phrases like "surface area of Class E airspace designated for an airport" do or don't include E4 "extensions"?
Related ASE questions:
Q: Why does the surface-level Class E airspace at SIT/PASI (Sitka Alaska) extend so far to the northwest?
Q: In the US, in actual practice, workload permitting, will ARTC facilities grant SVFR clearance for surface-level Class E "extensions" (E4 airspace)?
Q: Does an SVFR clearance extend to Echo surface extensions?
Q: What is the primary reason that the non-towered airports ACV, TVL, SGU, BIH, and SIT/PASI have E4 extensions to E2 airspace?
Q: Which parts of class E airspace can an ultralight (part 103) fly in without prior ATC authorization?
Q: What indication has the FAA given that phrases like "surface area of Class E airspace designated for an airport" do or don't include E4 "extensions"?
Q: Do the NPRMs & Final Rules preceding 1993 "alphabet" airspace re-designation indicate that these phrases were meant to exclude Class E "extensions"?
