This is not immediately obvious from the documentation(, which as it seems is often the case, was written for people who just like to read documentation, and not for people who are looking for answers).

The maximum sizes of the MySQL Blob fields are as follows:

Type What They Say It Needs That Means You Get
TINYBLOB L+1 bytes, where L < 28 256 bytes
BLOB L+2 bytes, where L < 216 65 kilobytes
MEDIUMBLOB L+3 bytes, where L < 224 16 megabytes
LONGBLOB L+4 bytes, where L < 232 4 gigabytes

There. Now it’s on the Internet and people can find the answer to this question. The world is a better place.