Is my work in data entry for construction projects of banks, hotels, or cinemas unlawful (haram)? And is this era a time when some forbidden things become permissible due to the scarcity of lawful (halal) options and necessity?

The basic principle concerning your work is permissibility, except for anything that involves aiding in sin, such as entering data for usurious banks, and forbidden hotels and cinemas; this is because these places were founded upon what is unlawful. It is not permissible for you to work in anything that involves aiding in sin. You are now faced with two options: continuing your work on the condition that you do not enter data for unlawful entities, or leaving your job and seeking another. For whoever abandons something for the sake of Allah, Allah will compensate them with something better, as stated in the verse: "And whoever fears Allah - He will make for him a way out And will provide for him from where he does not expect." As for the scarcity of the lawful and the abundance of the unlawful in these times, it is a trial, but whoever seeks the lawful will find it. Necessity permits prohibitions, but the limit of necessity is when one's situation reaches the point of perishing or near perishing if they do not engage in the unlawful.