Do "things" that are present depend on Dasein? I have read Being and Time, but a very long time ago. I am not sure if I mean present at hand, but I do mean in general anything that exists in the present moment. I am not sure why anyone would claim that everything that exists in the present moment depends on Dasein, but it seems to make sense if real entities do not have a tense.
The following quote refers to "fully fledged independent objects", i.e. independent of Dasein:
Stanford Encyclopedia of Philosophy - Heidegger 2.2.2 Modes of Encounter
When Dasein engages in, for example, the practices of natural science, when sensing takes place purely in the service of reflective or philosophical contemplation, or when philosophers claim to have identified certain context-free metaphysical building blocks of the universe (e.g., points of pure extension, monads), the entities under study are phenomenologically removed from the settings of everyday equipmental practice and are thereby revealed as fully fledged independent objects, that is, as the bearers of certain context-general determinate or measurable properties (size in metres, weight in kilos etc.). Heidegger calls this mode of Being presence-at-hand, and he sometimes refers to present-at-hand entities as ‘Things’.
In being present-at-hand these things exist in the present. However, in authentic temporality Dasein interacts in the present only in a moment of vision. This is the moment in which a formulated action is actually enacted, amongst the present-at-hand.
From Being & Time, ¶ 74· The Basic Constitution of Historicality
(H.338) Corresponding to the inauthentic future (awaiting), there is a special way of Being-alongside the things with which one concerns oneself. This way of Being-alongside is the Present - the "waiting-towards"; ... That Present which is held in authentic temporality and which thus is authentic itself, we call the "moment of vision". ... as an authentic Present or waiting-towards, the moment of vision permits us to encounter for the first time what can be 'in a time' as ready-to-hand or present-at-hand.