How can I prevent a paragraph break before placed inline content?

I answered this in your previous post: How does one place content relative to the page margin? - #2 by Andrew.

https://typst.app/docs/reference/layout/place/#effect-on-other-elements:

Overlaid elements don’t take space in the flow of content, but a place call inserts an invisible block-level element in the flow. This can affect the layout by breaking the current paragraph. To avoid this, you can wrap the place call in a box when the call is made in the middle of a paragraph. The alignment and offsets will then be relative to this zero-size box. To make sure it doesn’t interfere with spacing, the box should be attached to a word using a word joiner.