Does it say that there is a limit? Yes surely there is one, which most likely will depends on the Processor and OS you are running (64 bit or 32 bit), but anyway, such log varchars wouldn't be that recommended, and maybe the TEXT data type would be more suitable.
If you are used to MySQL you're used to a maximum limit because of MySQL will set a limit.
This kind of information is interesting if you're trying to understand PostgreSQL.
FWIW, we already started to use text :-)
B.
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