It is not about sign-ins or devices (could be inactive). What matters are simultaneous streams per service per subscriber (active use).
Apple TV+ would support up to 6 simultaneous streams per subscriber. That 6 is including all members of a Family Sharing group, so if such a group applies, then someone else might be taking your slots. This 6-limit would not apply to the free add-on for Apple Music Student (that is still 1 stream max).
Content from other catalogs will have different limits. Third party content providers will likely allow less simultaneous streams.
Download and stream shows, movies, and events from Apple TV+ and more - Apple Support
Buy-movies can stream on multiple devices. I don’t have enough devices to test and reach the limit for that.
Rent-movies can be streamed on one device at a time.
If it misbehaves, try force-quitting apps and/or restarting the devices. If it persists, try signing out for devices remotely. Check your Apple Account device list to find where you’re signed in - Apple Support. The list may show a device that you haven’t considered, perhaps?