Is there any official or at least widely recognized source that documents the visual parameters of music symbols? Something that says things like: "The note head shall be an ellipse with the proportion of the larger radius to the smaller radius of 51:35". Etc.
Yes. One of the most widely respected and utilized sources (at least in American universities and professional circles) for the precise parameters of standard notation is the book Behind Bars by Elaine Gould.
Many universities in the US have that book in their music libraries and several professional organizations, such as ASMAC, refer to that book as one of the standard texts on notation.
In the book, Gould does go into detail about the shapes and relative and absolute sizes for all of the most common musical symbols. It is a comprehensive text.
Excerpts related to your example:
The size of every notational symbol is measured in proportion to the stave size.
Table 2 on page 483 lists the traditional "rastral sizes" for staves for various uses. The sizes are the distance from the top line of a single stave to the bottom line. For piano music that is not for education (which is often printed larger), recommended staff size is between 6mm and 7.4mm. Note that piano parts written into a full orchestral score will usually use a staff size smaller than 6mm.
These are oval-shaped and placed on the stave with a diagonal slant away from the stem.
The height of the stave-space determines the size of all noteheads, which is crucial to ease of reading.
The notehead fills the space, touching the stave-line on each side of it, but without extending beyond either line.
Interestingly, Gould does not seem to detail the proportions of the "oval" for noteheads, so the specific example you asked about is not answered the book. It is clarified that the shape of a semibreve (whole note) is a wider oval than that of the minim (half note), which is in turn slightly wider than the black noteheads.
The Music Publishers Association published a style guide: "Standard Music Notation Practice". It does not address notehead size, but it does address other visual parameters. For example
Placement of note heads and accidentals: (a) Many musical symbols slant up from left to right at a uniform angle.
It also addresses issues such as stem lengths; beam thickness, placement, and angle; duration-based horizontal spacing; and relative placement of symbols like lyrics, dynamic markings, and other instructions.