Is working in an institution where there is intermingling (of sexes) and temptations, and shortening the beard, while being able to leave the job and receive a severance package that would cover debts and allow for starting a new business, lawful or unlawful?

Shaving the beard is forbidden except in cases of extreme necessity, while trimming it is permissible when there is a need. Unlawful mixing (of genders) at work is not permissible except in cases of extreme necessity. Necessity is defined as reaching or being close to a state of perishment (هلاك), and a need is not considered a necessity if it does not lead to perishment. The necessity that permits the forbidden is an existing one, not an anticipated one. Leaving work for the sake of Allah will lead to a better compensation.