Der `chem-angew`-Stil zeigt die DOI nur an, wenn der Eintrag keine Seitenzahl (in `pages`) hat. Die Idee ist, dass der Artikel dadurch trotzdem noch eindeutig und möglichst einfach identifizierbar ist.
Die beiden Einträge ohne `pages`-Feld in Deinem Beispiel haben beide zwar keine echte Seitenzahl aber eine elektronische Artikelnummer, die man in das `eid`-Feld schreiben kann. Leider kennt `chem-angew` das `eid`-Feld nicht, aber mit der folgenden Anpassung sollte es gehen
\documentclass{article}
\usepackage[ngerman]{babel}
\usepackage{csquotes}
\usepackage[backend=biber, style=chem-angew, doi=false]{biblatex}
\renewbibmacro*{note+pages}{%
\printfield{note}%
\setunit{\bibpagespunct}%
\printfield{pages}%
\setunit{\bibpagespunct}%
\printfield{eid}%
\ifboolexpr{ test {\iffieldundef{pages}}
and test {\iffieldundef{eid}}}
{%
\printfield{doi}%
\clearfield{doi}%
}%
{%
\iftoggle{bbx:doi}
{}
{\clearfield{doi}}%
}%
}
\begin{filecontents}{\jobname.bib}
@article{Cook.2006,
author = {Cook, R. James},
year = {2006},
title = {From the Academy: Colloquium perspective.
Toward cropping systems that enhance productivity and sustainability},
pages = {18389--18394},
volume = {103},
issn = {0027-8424},
journaltitle = {Proceedings of the National Academy of Sciences of the United States of America},
doi = {10.1073/pnas.0605946103},
number = {49},
eprint = {17130454},
}
@article{Tamburini.2020,
author = {Tamburini, Giovanni and Bommarco, Riccardo
and Wanger, Thomas Cherico and Kremen, Claire
and {van der Heijden}, Marcel G. A.
and Liebman, Matt and Hallin, Sara},
year = {2020},
title = {Agricultural Diversification Promotes
Multiple Ecosystem Services without
Compromising Yield},
volume = {6},
journaltitle = {Science advances},
doi = {10.1126/sciadv.aba1715},
number = {45},
eid = {eaba1715},
}
@article{FarreArmengol.2017,
author = {Farré-Armengol, Gerard and Filella, Iolanda
and Llusià, Joan and Peñuelas, Josep},
year = {2017},
title = {\textgreek{b}-Ocimene, a Key Floral
and Foliar Volatile Involved in Multiple Interactions
between Plants and Other Organisms},
volume = {22},
journaltitle = {Molecules},
doi = {10.3390/molecules22071148},
number = {7},
eid = {1148},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\begin{document}
Lorem ipsum\autocite{Cook.2006}
dolor\autocite{FarreArmengol.2017}
sit\autocite{Tamburini.2020}
Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua. At vero eos et accusam et justo duo dolores et ea rebum.\autocite{Cook.2006} Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet. Lorem ipsum dolor sit amet, consetetur sadipscing elitr, sed diam nonumy eirmod tempor invidunt ut labore et dolore magna aliquyam erat, sed diam voluptua.\autocite{FarreArmengol.2017}
At vero eos et accusam et justo duo dolores et ea rebum. Stet clita kasd gubergren, no sea takimata sanctus est Lorem ipsum dolor sit amet.\autocite{Tamburini.2020}
\printbibliography
\end{document}
\printbibliography
\end{document}
