As you say, integers are treated as exact by pari, while floating-point versions of the values have finite precision. The default floating-point η is larger than the number you're adding on.

Libpari and the Math::Pari package don't document this that I know of. Their documentation is generally specific to the functions available and sketchy for elementary properties of the native pari types.

In particular, the properties of floating-point representations are assumed to be familiar to the user. They are notorious for their inaccuracies. Floats aren't associative for addition, so they don't even form a mathematical group, much less a (finite) representation of the field of real numbers.