Overlap of site scopes is not a problem. I'm not sure if our scope is completely covered by History SE, or if some scientific developments wouldn't count as being historically significant there. But certainly there are a lot of good questions which could be asked on both sites. That said, this community has a major advantage going for it which keeps this site from being completely redundant. While our topic is narrower than that of History SE, we have people who are more specialized in this area, be they historians with interest in science, or scientists studying the history of their work. Expert questions within our scope—those that require considerable specialized knowledge and research to answer—are hopefully going to be more likely to find a satisfactory answer here than there. If not, there really is very little merit in this site existing at all. Luckily, I think we're accomplishing that so far, answering a large number of specialized questions that would have probably been less thoroughly answered on History SE or with a very different perspective.
As for other users asking questions on other related sites, this is not a problem. The only problem is if questions get cross-posted both here and on another site, because it becomes quite difficult to manage that situation. If a user asks on History SE and later decides they would rather it be here, they can flag for migration, but we shouldn't try to force this. If a question on History SE goes unanswered for several days and we think it would get a good answer here, it may be worth leaving a comment asking the OP if they'd rather it be migrated here, but there's no need to do this every question.
The total number of questions History SE has ever gotten on Mathematics or Science is 70 according to their tags (out of 3397 total questions). That's an insignificant amount, only around 2 per month. We have no need and little benefit to try to take those questions from them. It's much better to not annoy the users there with repeated comments of the form "this question would be better on HSM" for every single question related to science or math. Sure, some are good, but it's a very small volume overall and any crucial ones can be reasked here in a way more focused to this site. If users want to ask there, that's their choice. Most users will be able to find out that we exist if they are looking very hard (we appear right next to History in all the alphabetical lists). The added publicity from posting comments like this is negligible, and there are better ways to generate publicity (like community ads).
TLDR: The only real problem with the overlap here is that we have to watch out for cross-posts, which are not allowed.
For reference, this is the policy for most of the non-technology sites, where scopes do generally overlap some. For example, here's a meta Science Fiction & Fantasy post about the same thing in that context.
