In this proposal on the European Parliament website about Daylight Savings Time (DST), it is claimed that (emphasis mine):
Some studies indicate that summer-time arrangements could generate positive effects linked to more outdoor leisure activities. On the other hand, there are chronobiologic research findings that suggest that the effect on the human biorhythm may be more severe than previously thought. For instance, the Bundestag report of 2016 refers to findings which indicate that the human biological rhythm adjusts less well than previously thought to the spring clock change and that it may take certain chronotypes of people several weeks to adjust, while the autumn change poses fewer problems. However, the evidence on overall health impacts (i.e. the balance of the assumed positive versus negative effects) remains inconclusive.
By "the Bundestag report", they are referring to Bilanz der Sommerzeit conducted in 2014-2015, which claims (in German) that some people are still not adjusted after four weeks:
Mittlerweile gibt es vermehrte wissenschaftliche Anhaltspunkte dafür, dass sich die Anpassung der biologischen Rhythmen insbesondere an die Zeitumstellung im Frühjahr nicht so einfach vollzieht. Hier liefern neue Erkenntnisse Hinweise darauf, dass der Anpassungsprozess selbst binnen vier Wochen nach der Umstellung möglicherweise nur unvollständig bzw. gar nicht gelingt.
Meanwhile there are multiple scientific indications that the adaptation of the biological rhythm, in particular to the time change in spring, does not happen so easily. Here, new results deliver the indication, that the adaptation process may be incomplete even within four weeks of the time change, or that it does not succeed at all.
In the full PDF (213 pages, in German), they cite 5 scientific studies (Tab. V.1 on page 89) conducted between 1970 and 2006 (which makes me wonder what the EP means by "previously"). Some of those are based on self-reporting subjects, which I would fundamentally mistrust due to the placebo effect and the lack of a control, and others had very small sample sizes of less than 20 people. On page 90, the report admits that
Sämtliche Studien umfassten allerdings nur kurze Beobachtungszeiträume und meist nur sehr kleine Stichproben, sodass keinerlei wissenschaftliche Erkenntnisse darüber vorlagen, ob die durch die Zeitumstellungen hervorgerufenen Störungen im circadianen System über einen längeren Zeitraum anhalten und gegebenenfalls eine gesundheitsschädigende Wirkung haben können.
which translates to English as
However, each of the studies covered only short observation times and mostly only very small sample sizes, such that no scientific results are available about the question, as to whether the disturbances due to the time change in the circadian system remain over a longer period and could, if applicable, have a health-damaging effect.
Are there any quality peer-reviewed scientific studies, controlling for such effects as the placebo effect, that show that it does indeed take several weeks for some people to adjust to the spring clock change?
I am skeptical, because (1) many people in the world live near timezone boundaries and cross those regularly, (2) many people's times for sleeping and getting up vary by more than an hour in any regular week/weekend, and (3) (this is not a strong reason, but still) I don't even notice the time change.