You can have as many charts as you like on a tab. The key, I would say, is to maximize interactivity through the use of filter, slicers, & drill-downs as well as ensure that each chart on a tab adds value.
I work to ensure there is a clear purpose for each tab. E.g. I might have a tab to say how sales are doing. I have a single chart that's bigger and conveys that message, along with slicers (e.g. to slice by product or timeframe), and a few smaller supporting charts (that break down sales by region for example).
For pinning, you can pin either the entire tab or just individual charts from a tab. It sounds like you're doing the former, since you talk about minimizing the number of visuals on the tab. I lean towards the latter (since clicking on a chart will bring the user to the full tab anyway). I use pinned charts as a way to bring out the important metric from a report and make it front & center. E.g. I might have a report that allows you to dig into who is buying what, but I only pin the overall Sales number to my dashboard. If the sales number looks too low (or high), the end-user can click on it to get the full report and discover why.
When you pin a chart, the chart is pinned with all the slicers/filters currently in effect. So I only need one chart with a slicer for the store and I can pin "store sales" for any individual store by simply changing the slicer and pinning. I don't need a separate tab for each store. (Make sure to rename the pinned visual so you remember which store it is for.)
Pinning is only for dashboards, and my understanding is that Power BI Embedded only embeds reports (i.e. what's on your canvas). There is no pinning, and no dashboards, in Power BI Embedded.
Does this help answer your question?
