You don't need points 1-6 for a general definition. An urban forest is a forest growing within a city territory; it belongs to the green structures of the urban area.
I am sending you some examples of interesting articles from Poland. I think that after translation they will be useful for you.
Legal aspects of urban forestry in Poland and the concept of urban forestry and urban forests
Jaszczak R., Ważyński B., Wajchman−Świtalska S. 2017. Prawne aspekty leśnictwa miejskiego w Polsce. Sylwan 161 (8): 659−668.
Recreational development zones in forests within the reach of cities
Jaszczak, R., 2008. Las i gospodarka leśna w zasięgu oddziaływania miast w Polsce. Studia i Materiały Centrum Edukacji Przyrodniczo-Leśnej, 10(3 [19), pp.152-171.
Principles of management of urban protection forests (Good practice project in shaping the urban forests)
Wołkowycki, D., 2022. Rozdział 14 Zasady kształtowania lasów ochronnych miast. In: Lasy przyszłości. Wyzwania współczesnego leśnictwa / Marozau Aleh, Wołkowycki Dan (eds.), 2022, Oficyna Wydawnicza Politechniki Białostockiej, ISBN 978-83-67185-46-2 , pp. 157-174, DOI:10.24427/978-83-67185-47-9_14
Other helpful from Poland e.g.
Wajchman-Świtalska, S., Zajadacz, A., Woźniak, M., Jaszczak, R. and Beker, C., 2022. Recreational Evaluation of Forests in Urban Environments: Methodological and Practical Aspects. Sustainability, 14(22), p.15177.
Referowska-Chodak, E., 2019. Pressures and threats to nature related to human activities in European urban and suburban forests. Forests, 10(9), p.765.
The urban forest does not have a standard area. It includes all the islands of forests, plantations, gardens (botanical or hut) or the trees of alignments on the streets, public places etc...
It has a great floristic diversity.
It is therefore a forest to be considered a lot in the conservation of terrestrial biodiversity.