Is an Embassy or Consulate "foreign soil"

Embassies and Consulates do not constitute separate territory or "foreign soil".

Certain diplomatic provisions and niceties are set out in the 1961 Vienna Convention on Diplomatic Relations (UN, Treat Series, vol500 p. 95) but the granting of territorial jurisdiction is not among them.

The US Court of Appeals case of McKeel v. Islamic Republic of Iran, 722 F. 2d 582 - Court of Appeals, 9th Circuit 1983 is of assistance.
Sneed J. had to interpret whether the US embassy in Tehran was subject to the jurisdiction of the US and concluded it was not at paras. 16
and 20:

… the issue before us is whether the embassy in Tehran is "territory ... subject to the jurisdiction of the United States."
Appellants contend that it is. Territory, of course, is a primary basis for jurisdiction, i.e., a state may prescribe and enforce a
rule of law for conduct occurring in territory under the state's sovereignty. Restatement (Second) of the Foreign Relations
Law of the United States Secs. 10, 17, 20 (1965) [hereinafter cited as Restatement (Second) ].7 A United States embassy,
however, remains the territory of the receiving state, and does not constitute territory of the United States.
Restatement (Second) Sec. 77 comment a. Thus, United States embassies are not within the territorial jurisdiction
of the United States. See Meredith v. United States, 330 F.2d 9, 10-11 (9th Cir.), cert. denied, 379 U.S. 867, 85 S.Ct. 137, 13
L.Ed.2d 70 (1964).
…
…The general rule is that "legislation of Congress, unless a contrary intent appears, is meant to apply only within the
territorial jurisdiction of the United States." Foley Bros. v. Filardo, 336 U.S. 281, 285, 69 S.Ct. 575, 577, 93 L.Ed. 680
(1949); see also Meredith, 330 F.2d at 11. Because United States embassies are not subject to the territorial jurisdiction of
the United States, the district court correctly held that the FSIA does not provide jurisdiction over Iran in this case.10II.
[Footnotes omitted and emphasis added]

It seems that even a reputable/newspaper "of record" relies on perceptions or common but incorrect beliefs. Here's the Globe and Mail take on the the murder/disappearance of journalist Jamal Khashoggi:

Such a search would be an extraordinary development, as embassies and consulates under the Vienna Convention are technically foreign soil. Saudi Arabia may have agreed to the search in order to appease its Western allies and the international community.

This is what happens when people rely on the Simpsons for international law insight.