A lot of professional musicians memorize tons of music habitually. It's not very hard to be completely honest.

Mozart only wrote like 20 piano sonatas and about the same number of violin sonatas. It's no exaggeration to say that most concert pianists or violinists probably know at least 5 of them just as a matter of course because they will have learned them at some point in their musical education and someone who specialised in the classical period would probably know all of them. My wife learns tons of repertoire when she's performing as most of her concerts are completely from memory and this includes a vast range of repertoire from the middle ages through very complex 20th/21st century music.

Conductors often memorize monumental works as part of their preparation. Eg Zubin Mehta conducting Bruckner's 8th from memory age 89. That's a way way bigger piece of music than a Mozart sonata - super long and with massive forces. https://parsikhabar.net/music/zubin-mehta-at-89-still-comman...

This is the same as how chess grandmasters know literally hundreds or possibly thousands of games. Extreme example: David Howell tests Magnus Carlsen https://youtu.be/eC1BAcOzHyY?si=I-xJEo4NQUkLPDQ0

...or jazz musicians know hundreds or possibly thousands of standards.

You kind of have to know these things to perform. That being said with memorizing music you have a lot of structure that makes it easier whereas memorizing digits of pi or e you are learning a transcendental number so it may as well be random. You have to impose whatever structure you can, which must surely make it harder.