The Ptolemies by this stage of the Hellenistic period would be masters of using the various images and symbols that collectively made up their rather diverse society. While the most important thing for a Ptolemaic king/queen to do is to make sure your Greco-Macedonians are well and truly happy. The native Egyptian population largely outnumbered this Greek speaking minority, but the latter held the political power of the state (since essentially it was created via Ptolemy I, a Macedonian general, who claimed Egypt as "won by the spear" as Diodorus Siculus would put it).

To the Greco-Macedonians, Cleopatra VII would be seen as another ruler in the line of the Ptolemaic dynasty, a decisively Macedonian one (while there is no equivalent to a basileos, the military and nobles would see her as the queen once her brothers were taken care of and she was fully in power). I don't want to get too wrapped up in the semantics on whether Macedonian is truly different from Greek especially by this point, but let's assume that the Macedonians *are* greek, but still different enough for each other to differentiate themeselves (think of Texans and New Yorkers, as they are both "Americans" and speak the same language, but they still have their own cultures and "separate identity" if you truly asked them). Author/Professor Sarah B Pomeroy's "Women in Hellenistic Egypt" talks about how the practices of Cleopatra were very reminiscent of her Macedonian forebears, such as using the Greek language for administration, practicing horseriding (something unthinkable for any respectable Greek woman) and just generally acting as a classically educated elite.

The Egyptians serving under her, while not perhaps truly viewing the Ptolemies as Egyptian Pharaohs, were comforted considerably by the use of familiar images and symbolism. At this stage, all of the Hellenistic monarchies had appropriated a lot of the non Greco-Macedonian gods, titles and images in order to more smoothly insert themselves into the long monarchical history of the Near East and Egypt. The degree to this varied, but the Ptolemies had long used the story of Isis and Osiris, the married sibilings of the Egyptian pantheon, to represent themselves (as they too were prone to royal incest) as legitimate heirs of the pharaonic tradition, along with instituting various "fusion cults" like Serapis to better integrate Greco-Egyptian beliefs. Cleopatra was unique, however, because she had strongly appealed to the Egyptian people, such as her learning of the native Egyptian language (the first known Ptolemaic ruler to do so in over 250 years of rule!). It cannot be taken too far to imply that Cleopatra had "gone native", if such a term is appropriate, since she continued to represent herself as a Macedonian style queen above all else. She had just taken further steps to continue a tradition that had been practiced to some degree by her forebears.

With the Romans, we run into a bit of a problem. Augustus' victories in the civil wars and his celebration of instituting "peace" came with a caveat: celebrating victory over other Romans (i.e. Marcus Antonius) was not something that was acceptable. So the defeat of Antonius turned into vanquishing an evil oriental/decadent Eastern Greek queen, and most of the sources (Plutarch, Appian, etc.) tend to reflect the negative corrupting influence of Cleopatra on Antonius. We thus need to take their view on Cleopatra with a heavy grain of salt. Romans failed or didn't care to recognize the differences between Greeks and Macedonians, preferring to just to label any Hellenistic ruler as "Greek", but also emphasized their adoption of foreign traditions to highlight why these kings were despotic tyrants (eg. the Seleucids as "asian" or "syrian"). Thus Cleopatra's "Easterness", whether it was seen as Egyptian, Greek or something in-between, made her foreign and corrupting, and thus a justifiable reason why Augustus was right to conquer Egypt into a new province for the Empire.

TL:DR, She was a Macedonian queen to her Greco Macedonian subjects, a Macedonian queen to her Egyptian subjects (but one that was much more friendly to Egyptian customs and beliefs than most of her predecessors), and to the Romans she was seen as another oriental despot with Greek/Egyptian tendencies (but who really cares what exactly she was in comparison to the virtus of Rome?)

Some useful sources you may like to read
Sarah B Pomeroy - "Women in Hellenistic Egypt: From Alexander to Cleopatra"
Adrian Goldsworthy - "Antony and Cleopatra"
Stacy Schiff - "Cleopatra: A Life" (Have not read, but have heard good things about)