ELI5: is it true that Base58 doesn't prevent typo, but Base58check does, really because there is a checksum?
Yes. Every byte sequence corresponds to one Base58 string. Every byte sequence also corresponds to one Base58Check string, which contains a 4-byte redundancy, a checksum.
And this 4-byte-code's only purpose is the detection of transmission errors (typos). Newer Bech32 addresses have a different kind of checksum allowing error correction, up to a certain level in addition to error detection.