Some Processing models are so intrinsically linked to the logic inside a particular project that they have no meaning (or are totally broken) outside of that project (e.g. models which rely on the presence of particular map layers, relations, etc). Accordingly, from QGIS 3.4, Processing models can be stored inside QGIS project files. Any models stored within a project are made available as soon as that project is opened. This also avoids avoid cluttering up the "global" model provider with models which make no sense, and makes it easier to distribute a single project all relevant models included.
Models are stored inside projects by clicking the new "Embed in Project" button in the Modeler dialog toolbar. Models can be removed from a project from the model's right click menu in the toolbox.