Pretty much every font format in common use today (OpenType, TrueType) is limited to 64K uniquely encoded glyphs. That is 65,535 glyphs plus notdef. But Unicode has more than twice that many characters encoded. This makes it impossible to properly encode all 149K+ current Unicode characters in a single font, or even in two fonts.
So, a single font maxes out at less than half of Unicode (ignoring multiply-encoded glyphs, admittedly). What that means is that you need a set of two or more fonts in the same style.
Of such families/typefaces, Noto / Source Han Sans (same typeface, two names) by Google, Adobe and partners has the largest character coverage currently, and is still being actively developed. There are over 77,000 characters in the Noto font set.
Adobe’s release as Source Han Sans is precisely at the 64K glyph encoding limit of the OpenType format! It is quite the font engineering feat. Being an OpenType font (or set of OpenType fonts, depending on your version) it is widely supported across major platforms such as Windows, macOS, UNIX/Linux and Android. (Current exception: the color emoji portion doesn’t work everywhere.)
As discussed, the Noto font/family already has more glyphs than fit in a single font. For now, people will switch fonts—or use multiple fonts with fallback, or “virtual font” mechanisms, to combine the fonts, if that is really needed.
In practice, there are large swathes of Unicode that are very rarely needed by “normal” users, so separate fonts is not a huge problem. Creating fonts in a consistent style across many writing systems and groups of symbols is the hard part!
Although the Noto family is very large, and well designed, it might not be the biggest character coverage….
The Code 2000 series of fonts by James Kass has ~ 90,000 glyphs. (Some East Asian languages share the same character codes but draw the glyphs differently.) Code 2000 was the original font, with ~ 63K glyphs, while Code 2001 and Code 2002 add further glyphs in the same design, as well as repeating some. It may have more unique glyphs than Noto, and also covers some non-Unicode writing systems such as Tolkien’s Elvish languages and Star Trek’s Klingon.
Unfortunately, the design of Code 2000 is best described as “quirky” at best, and there is only one style, so for the languages that benefit from bold and italic, you’ll just get fake bold and fake italic from your computer, magnifying the existing visual issues. But it is an amazing achievement for what seems to be a single person, as far as I know.
An honorable mention that covers a major portion of Unicode and approaches the 64K-glyphs-per font limit: GNU Unifont is a bitmap font (unlike today’s “normal” scalable outline fonts, and not supported by all operating systems) that has ~ 63,449 glyphs and approaches the format maximums.
Another honorable mention would go to Arial Unicode MS, which has over 50K glyphs, and has both a regular and a bold version.