Apodization filters have been around photography for a long time. Often they are called "soft focus" filters. Lenses that include such filter are sometimes called "soft focus" lenses.
Lower quality, non-apodizing "soft focus" filters are basically diffusion filters that also reduce contrast and result in softening the overall image. Higher end "soft focus" filters, such as the Zeiss Softar line, let center light through undiffused and only diffuse the light entering the edges of the lens.
This is the basic concept of apodization: Allow all of the more collimated light to pass through the center of the lens while allowing some, but not all, of the less collimated light from the edge of the lense to pass. Stopping down a normal lens would only allow the light through the center, but not allow a portion of the more diffused light from the edges of the lens.
Rather than use material that diffuses light, such as some soft focus filters do, apodizing lenses use either a ring of neutral density material that is more dense near the edges than at the boundary nearer the center where all light is allowed to pass or they use plates with holes of various sizes and patterns near the edges.
The classic early soft focus lens was the Rodenstock Imagon made to fit in the lens board of a Large Format view camera. Introduced in 1930/31, it was in production until the 1990s. It had a set of different "sink strainer" aperture diaphragms, a/k/a apodization filters, that included a main opening in the middle that produced the relatively sharp image. Each "sink strainer" also had smaller holes of varying sizes and patterns around the edges of the various diaphragms that could "dial in" the amount of soft focus that was blended with the sharp image projected through the center hole in the diaphragm.
Combined with uncorrected spherical aberration/field curvature that made the focus distance at the edges closer to the camera than the focus distance at the center of the lens' optical axis, this allowed the proportions of 'in focus' versus 'soft focus' light to be controlled.
Fuji also produced such a lens for 135 format (35mm) cameras way back when, although the pattern was fixed and inside the lens, rather than on the front of a Large Format/Medium Format lens such as the Rodenstock.
Other soft focus lenses, such as the discontinued Canon EF 135mm f/2.8 Soft Focus (with Softfocus mechanism) used different mechanics to do the same thing: combine in-focus light coming through the center of a lens that had uncorrected/undercorrected spherical aberration/field curvature with softer light entering through the edges of the lens in a way which could be more variably controlled than by a traditional lens design with a single opening in the aperture diaphragm.
In addition, one can simulate the look digitally by placing layers with varying levels of simulated spherical aberration applied to them in various amounts of transparency/opacity on top of the in-focus base image.