Hi Rae,
Thanks for the questions. Yes, having enough materials and activities to keep children engaged would count under the marker "anticipates challenging behaviors or escalation" in Proactive for BM and can count in Variation in Approach in ILF.
The scoring note here is more about specific engagement strategies that educators use such as making story time interesting by asking questions and having children act out moments from the book, by using questions to support continued exploration, or by giving preview or reorientation statements so children know how to focus their attention. These strategies are more for the purpose of engagement, which then has an effect on behavior (as behavior challenges are less likely to occur when children are engaged).
The bigger question here is about overlap. When these questions arise, remember the definition of the indicators and dimensions. This can help in deciding which indicator a behavior falls in. If the behavior is helping keep children engaged (keep their attention), then it goes in ILF. If the behavior helps to reduce behavior issues, then it goes in BM. If it fits in both (such as in this case of making sure there are materials to keep children engaged and enough of those to prevent conflict over materials), then it can go in both.
It may also help to look at what other behaviors or statements are happening around that. Does the educator say, "There are plenty of markers so you should each have enough to draw" and "If you want another color, you can ask a friend to share?" Those statements indicate that the educator is trying to prevent conflicts around the markers and outline clear expectations. Or the educator might say, "We have lots of different colors so you can really use your imagination" which is more of an engagement strategy to encourage them to use the hands-on materials.
I hope that helps. Happy to clarify more if needed.
Vicki