endless; boundless; there’s no end to ~
Expresses that something is endless, boundless, or has no end in sight.
This pattern is used to say that there is no end to something, often implying that it's futile or frustrating to try to deal with it all. It can follow the て-form of a verb to indicate that doing that action repeatedly or endlessly is pointless because you'll never finish. It can also follow a noun with が to say that the noun itself is boundless or infinite.
It carries a tone of resignation or complaint. For example, if you say 仕事がたくさんあって切りがない, you're moaning that there's too much work and you'll never see the end of it. The nuance is that the situation is overwhelming, and trying to complete it is like chasing the horizon.
This is a fairly conversational expression, though it can appear in writing. It's not rude, but it's best used in informal or semi-formal contexts. At N1 level, you'll encounter it in narratives and conversations alike.