Yeah this is a really tough one. Power BI embedded is actually REALLY hard to work with because it's intricately tied into the Microsoft Authentication platform. You need a deep dev skillset and a solid understanding of how OAuth2.0 works, and even then, there are a lot of "gotchas" that are not mentioned in the Power BI documentation when it comes to embedding Power BI content and keeping it authorized over long periods of time. That, and Microsoft Auth is just plain hard.
I am speaking from experience because I run a 3rd party dedicated Power BI digital signage app called Displagent, and this has been my life's work for the past two years. It's very difficult, and it's taken a lot of work for me to learn the ins and outs of all of this.
In my app Displagent, I made a huge focus on keeping users logged into Microsoft over long periods of time so that people can setup slideshows and digital signage on their TVs, fire them up, and then forget about them/not worry about them and just let them run continuously. Sounds like the scenario that you are describing.
In my app, I offer two types of integrations: the Standard Integration and the Advanced Integration. You can read my doc pages for more info, but basically the first uses the MSAL auth library, and the second uses a line-of-business Azure App Registration that you have to make in your Azure tenant. Either way, both work extremely well and are able to keep users logged in for long periods of time. The Advanced Integration in particular works exceptionally well, my users never have timeouts/sign out problems.
Power BI digital signage and Power BI embedded are surprisingly difficult for most companies. If you're a dev and want to do this yourself, I'm happy to offer more info/lessons that I've learned. But forewarning, it's all very involved and quite cumbersome (again, speaking from experience). If you want to save yourself the time and trouble, feel free to checkout my app or ask me some questions.
