What does it mean to say that space has three dimensions? It means that space has directions that have three dimensions, that is, three degrees of freedom. The dimensions are the directions in the space.
It’s not that there are some dimensions that are spatial and others are something else but that space is characterized by a certain number of independent directions. That is why three coordinates are needed to specify locations in space.
Saying that time also has three dimensions does not mean time has three different dimensions. It means that time also has directions that have three dimensions, that is, three degrees of freedom. The dimensions of time are the directions in time.
Vectors have magnitude and direction. A position vector specifies a location in multiple dimensions. Whether that location is in time or in space depends on the units of the magnitude. If the units are length, the vector is in space. If the units are durations, the vector is in time. If the units are lengths per unit time, the vector is in spacetime. If the units are newtons, the vector is in a force field.
Vectors have directions, and directions have dimensions.