The client/owner of the business has to answer the question - "What do people search to find a product like theirs?" Do they search for the attributes of the product, or what it does? And something along those lines.
"Mosaic Software" is very generic, yes. But it's not unthinkable to use that as H1. If they have a unique offering and a good enough brand recognition, maybe people will actually search for "mosaic software." For example, people search for the brand name, snapchat, not for a video/social app. Or, KPMG, not management consultants. Those are extreme cases, but that's just to make the point.
Something else to think about: H1 is important, no doubt, but your primary targets should be the title and description meta tags -- these are what the users see in search results. These are two important hooks that will get users to click on your link, and once they are on your page, only then will they see the works of the H1 tag. Some site keep H1 and title same, but you can get creative with it. Here's an example with different H1 and title: title is keyword-rich, h1 is just that, the story title. https://mashable.com/2018/04/13/trump-deleted-john-kelly-face-palm-tweet/.
An example in commerce/software space: https://www.semrush.com/. Notice the diff. between h1 and title.
In your case, the title, can be a hybrid of the two options, e.g., "Software for the production chain of metallurgical products | Mosaic software". Then add finer details with relevant keywords in the description tag. While you are at it, keep the URL also saturated with good keywords.
Then comes the H1 tag. Don't use H1 tags only for keyword stuffing. Use it to craft a good article title with only those few good keywords that actually deserve a spot in H1 tag.
Your second question on H1 inside div tag: it won't look right. It will break it into two lines because H1 is a block level element, meaning, it will live like a king in its own line, below "Our most advanced."