Don't treat your open source project like a dirty secret
If you're making the investment in developing and maintaining an open source project in addition to your commercial product, you should make sure that the open source project is providing value to your company.
There are many ways that an open source project can help a startup grow. It can drive awareness, it can help you get feedback more quickly, it can help your technology become the standard in your particular niche.
But if you want your open source project to provide value to your company, it needs to be pretty obvious that your open source project is connected to your company. There's no reason an open source startup should not proudly show off its project on the homepage. And while you definitely don't want to push your commercial product on your open source community, don't treat it like a secret, either. Open source users shouldn't feel pressured to use the commercial product, but they should all know that it exists.
It also should be clear how the open source project and the commercial product relate to each other. Who is right for open source only? Who is right for the commercial product? Make it easy for people to understand this and self-select either way.
How open source projects can provide value is the topic for another day. But regardless, they won't do much for the company if the project is kept so separate that people don't realize the two are connected.