Is a Muslim residing in Europe sinful if he does not directly and explicitly invite his non-Muslim colleagues to Islam, even though he adheres to honesty and trustworthiness, lowers his gaze in his dealings with them, and utilizes available opportunities in side discussions to talk about Islam?

Calling people to Allah is a collective obligation upon the Muslim community (fard kifaya). If no one undertakes it, then it becomes an individual obligation (fard ayn) upon whoever is able, according to their capacity and knowledge. Da‘wah is not restricted to one method; rather, the most effective way to guide those being called should be adopted, whether it is direct or indirect. So, if there is no one else to call them but you, then it becomes obligatory upon you to call them.