Air carrier pilot reported descending too low during visual approach and receiving an aircraft terrain warning as a result of entering the wrong altimeter setting. Flight crew continued approach and landed.

Narrative

On flight XXXX from ZZZ-ZZZZ I inserted the wrong altimeter setting and got low on a visual approach that was backed up by RNP to Runway XX at ZZZZ. This happened due to a combination of errors that we as a crew allowed due to the ease of flying in VFR conditions.When I set up for the approach; we were too far out to receive ATIS from ZZZZ. I used the weather from FD Pro X app and can only guess that I had old weather due to losing the internet connection earlier in the flight. My First Officer (FO) was not able to get weather due to no internet and I input my weather. We planned to get ATIS when closer to the airport; but on arrival we were given multiple slow downs on the decent and were talking about making the crossing restrictions. When on the approach and visual with the airport we started our final descent to landing and I realized that we were low. There is a large drop off just prior to landing on Runway XX; so I delayed leveling off in case it was a visual illusion. I eventually clicked off the Autopilot and called for flight directors off. At the same time we received a warning of 'too low'. It went away as soon as we crossed the ridge line to the depression prior to the runway. We landed uneventfully.