The electron is an elementary particle in the standard model of particle physics. As such it is postulated to be a point particle. BUT this is quantum mechanics, the term particle is just a tag on a quantum mechanical entity.
Quantum mechanical entities follow boundary conditions in completely determined solutions of quantum mechanical equations. Within these solutions they are described by a function F(x,y,z,t) but this is a complex function and can acquire a physical meaning within an expectation value of a position operator or a momentum operator, which involves the complex conjugate squared,. It is a postulate of quantum mechanics that this is a probability density for finding the electron. One has to do many measurements with the same boundary conditions to get the probability distribution.
In the case of the double slit single electron at a time one can see the probability density developing because the electrons are not in a bound state. A single electron interacts with the screen and leaves a point characteristic of a classical particle. It is not spread out over the whole pattern.
Electrons in atoms are described by the orbitals and as Conifold has referred also the Hydrogen orbitals have been measured in a specific experiment:
It is a probability density distribution, a collective measurement of interactions with photons
After zapping the atom with laser pulses, ionized electrons escaped and followed a particular trajectory to a 2D detector (a dual microchannel plate [MCP] detector placed perpendicular to the field itself). There are many trajectories that can be taken by the electrons to reach the same point on the detector, thus providing the researchers with a set of interference patterns — patterns that reflected the nodal structure of the wave function.
The x and y coordinates are in mm on the detector plane.
The color coding is the intensity registered at the detector. A point on the plot builds the interference patterns of the position of the electrons. In a sense , the double slit interference pattern reflects the geometry of the two slits and one could arrive at the geometry by using the pattern. The interference pattern seen above can be correlated with the calculations of the orbitals. For details the paper can be seen here.
From this data an estimate within the Heisenberg uncertainty could be made of the position of the probable d(V) of the electron in the atomic dimensions but as the hydrogen atom has a complete quantum mechanical solution, one uses the mathematics of orbitals.