Your sentence sounds perfectly natural to me. The general sense that slid/slide imparts to movement is that of smoothness, usually in contact with something. This could be describe literal, physical movement (lack of friction) or figurative movement, in a social or potentially digital sense. A couple other examples:
I turned off the lights and slid into bed. (describes movement of the speaker)
After a few tweets back and forth, I slid into his DMs (direct messages) for a more private conversation. (this one is informal and somewhat colloquial, describing the movement of the conversation)
I felt a sense of dread as the meeting slid further and further into chaos. (describes the movement of the meeting in terms of its productivity changing)
As my bowling ball slid down the lane, I was sure I would get a strike. (physical movement)
In many cases, certainly those in this question, "slide/slid into" can be replaced with "slip/slipped into".