What does « To engage / To plunge into » mean in the Quran?

And it has already come down to you in the Book that when you hear the verses of Allah [recited], they are denied [by them] and ridiculed; so do not sit with them until they enter into another conversation. Indeed, you would then be like them. Indeed Allah will gather the hypocrites and disbelievers in Hell all together -

And when you see those who engage in [offensive] discourse concerning Our verses, then turn away from them until they enter into another conversation. And if Satan should cause you to forget, then do not remain after the reminder with the wrongdoing people.

And they did not appraise Allah with true appraisal when they said, "Allah did not reveal to a human being anything." Say, "Who revealed the Scripture that Moses brought as light and guidance to the people? You [Jews] make it into pages, disclosing [some of] it and concealing much. And you were taught that which you knew not - neither you nor your fathers." Say, "Allah [revealed it]." Then leave them in their [empty] discourse, amusing themselves.

And if you ask them, they will surely say, "We were only conversing and playing." Say, "Is it Allah and His verses and His Messenger that you were mocking?"

[You disbelievers are] like those before you; they were stronger than you in power and more abundant in wealth and children. They enjoyed their portion [of worldly enjoyment], and you have enjoyed your portion as those before you enjoyed their portion, and you have engaged [in vanities] like that in which they engaged. [It is] those whose deeds have become worthless in this world and in the Hereafter, and it is they who are the losers.