Is Haiku a Unix-like operating system?

It is Unix-like but the filesystem layout is different and a /home you used for another Unix system will likely not work.

In fact here is what the POSIX spec says about a home directory:

" If no directory operand is given and the HOME environment variable is empty or undefined, the default behavior is implementation-defined and no further steps shall be taken." (https://pubs.opengroup.org/onlinepubs/9699919799/utilities/cd.html)

It may be more liberal than you expect if you are used to the much larger common feature set between Linux and BSD, for example.