Like other Autodesk software, BIM 360 projects are version specific which can cause some confusion.
Even though permission to access a Revit project on BIM 360 may be given, it is common for that project not to show up in the Revit home screen under the BIM 360 project list for users that have been given access.
The issue lies with versioning, the Revit version that was used to start the project in BIM360 Design dictates the version going forward. If you navigate to the project admin section>Services>Document Management> Revit Cloud Model Upgrade, you can clearly see the versioning of the project. If a project is started using 2019 software, then it will not be visible in the 2020 version of that software.
Once you know the correct versioning of the product then you can open the corresponding software to gain access. Within BIM 360 there is the option to upgrade multiple models to a newer version. Special care should be taken when using this command as all participants in the project must agree before this change is made. Once a Revit file has been upgraded there is no reversing the process.
In order to minimise errors, the Revit version installed on all of the machines that are working on work shared files must be the same and verified. Users in older versions may reintroduce previous issues that have since been fixed by product updates. Avoiding multiple syncs at the same time is also an important aspect of using BIM 360, In Revit 2020 and later there is a BIM 360 Design indicator on the status bar to indicate whether the model is being synced or not. It is also good practice to close Revit about once every 4 hours to clear its memory.
The Autodesk Desktop Connector is used to link non-cloud-based work shared Revit models. BIM 360 Drive is used to link cloud-based models. When a central file with non-cloud work shared Revit models will be published, the non-cloud shared models will not be visible in BIM 360 Web Browser.