During a long press, on native iOS the context menu does not show until the long press has ended. The handles are shown immediately when the long press begins. This is true for static and editable text.

For static text on Android, the context menu appears when the long press is initiated, but the handles do not appear until the long press has ended. For editable text on Android, the context menu does not appear until the long press ended, and the handles also do not appear until the end.

For both platforms in editable/static contexts the context menu does not show while doing a long press drag.

I think the behavior where the context menu is not shown until the long press ends makes the most sense even though Android varies in this depending on the context. The user is not able to react to the context menu until the long press has ended.

Other details:
On a windows touch screen device the context menu does not show up until the long press ends in editable/static text contexts. On a long press hold it selects the word on drag start as well as popping up the selection handles (static text).