TLDR version (summarizing what I found out so far):
- On the issue of the 11th amendment (sovereign immunity), the clear harbinger appears to be Seminole Tribe v. Florida (1996)
- On the 10th amendment and the Commerce Clause, it looks like New York v. U.S. (1992) was the harbinger
- More tenuously (because the cases involving it were much more diverse), on the 14th amendment, the harbinger might have been Gregory v. Ashcroft (1991)
According to Chemerinsky (2002)
Without a doubt, the greatest changes in constitutional law in the last decade have been in the area of federalism. The U.S. Supreme Court has significantly limited the scope of Congress’s powers under the Commerce Clause and pursuant to section 5 of the Fourteenth Amendment. Additionally, the Court has revived the Tenth Amendment as a limit on federal authority. The Court also has greatly expanded the sovereign immunity of state governments and has barred suits against them in state and federal court. Virtually all of these cases have been decided by a 5-4 margin, with the five most conservative justices—Chief Justice William Rehnquist and Justices Sandra Day O’Connor, Antonin Scalia, Anthony Kennedy, and Clarence Thomas—in the majority.
Although the cases can be fairly easily identified, talking of a harbinger means that there is some kind of connection between cases, and this isn't always straightforward to establish. Skipping [for now] the most famous cases of the Rehnquist court and starting with a more obscure line, in which a harbinger can be identified:
A[...] key aspect of the Court’s federalism decisions has been a substantial expansion of state sovereign immunity. In Seminole Tribe v. Florida, 517 U.S. 44 (1996), the Court held that Congress may authorize suits against state governments only pursuant to section 5 of the Fourteenth Amendment and not under any other congressional power. [...]. It was based on this decision that the Court handed down the rulings [...] in Florida Prepaid, Kimel, and Garrett, that state governments could not be sued for patent infringement, violating the Age Discrimination in Employment Act, or infringing on Title I of the Americans with Disabilities Act. Also, in Alden v. Maine, the Court held that state governments cannot be sued in state court, even on federal claims, without their consent. [...]. In Federal Maritime Commission v. South Carolina Port Authority, the Court ruled that state governments cannot be sued in federal agency adjudicatory proceedings without their consent.
Chemerinsky fails to make explicit an example of the Tenth Amendment revival in his article, but one is well-known (and used in the article as source of quotes for the Rehnquist court ideas on the separation of powers); in Printz v. United States (1997) provisions of Brady Act commandeering sheriffs to perform background checks were deemed to violate the Tenth Amendment. I don't [yet] know if this was the first case of the Rehnquist court reviving the Tenth Amendment.
As for limiting the Commerce Clause, again Chemerinsky doesn't have a very clear timeline, but he quotes from (again for ideas on separation of powers) another famous case: United States v. Lopez (1995), in which The Gun-Free School Zones Act (GFSZA) was deemed unconstitutional because it didn't really involve commerce, so basically Congress acted ultra vires in justifying it by invoking the Commerce Clause. In a later case, also pretty famous, United States v. Morrison (2000) the court ruled that neither the Commerce Clause nor the Fourteenth Amendment could justify the provision of the Violence Against Women Act (VAWA) that victims of gender-motivated violence had the right to sue their attackers in federal court.
That leaves us with finding a harbinger the Fourteenth Amendment series. Interestingly, the first case (mentioned by Chemerinsky, but again just for quotes on the court's ideas of separation of powers) appears to be Gregory v. Ashcroft (1991), in which the Supreme Court decided that Missouri's law of age-based mandatory retirement for its judges violated neither the Fourteenth Amendment's Equal Protection Clause nor the federal Age Discrimination in Employment Act (ADEA). This case was less controversial, a 7-2 decision. It's also a bit more obscure, if we go by its lack of a Wikipedia page.
Also note that there several book-length treatments of the topic; for a review up to 2010 see Dinan (2010). There's Blanks and Blakerman (2012) who also cover the Roberts court (up till then).
Actually Dinan gives a more likely harbinger for the Tenth Amendment series (certainly preceding Printz):
Amendment was invoked to prevent Congress from commandeering state and local
legislators and executive officials, thereby invalidating a provision of the Low-Level
Radioactive Waste Policy Amendments Act (New York v. U.S., 505 U.S. 144 )
Looking at its Wikipedia page, this 1992 case involved the Commerce Clause as well, so it's a harbinger for that series too (preceded Lopez).
And if one is looking for harbingers before Rehnquist court, these are indeed hard to find (also validating the OP's quote/basis) with a concrete analysis, from Dinan:
the Rehnquist Court issued a number of high-profile invalidations of
congressional statutes, and this was all the more significant in that only two congressional
statutes were overturned on federalism grounds in the half-century prior to Rehnquist
assuming the role of Chief Justice, and both rulings were soon reversed. In 1970, in a
decision overturned the next year by the 26th Amendment, the Court held that in lowering
the voting age to eighteen in state and local elections as part of the Voting Rights Act
Amendments passed that year, Congress exceeded its enforcement power under the 15th
Amendment (Oregon v. Mitchell, 400 U.S. 112 ). And in 1976, the Court relied on the
10th Amendment to prevent Congress from enforcing the overtime provisions of the Fair
Labor Standards Act against state and local governments (National League of Cities v. Usery,
426 U.S. 833 ). This was reversed nine years later when a bare majority of Justices
swore off the need for judicial enforcement of federalism because state interests were seen as
adequately protected in the political process (Garcia v. SAMTA, 469 U.S. 528 ).