Best way to connect 2 pins that are next to each other?

A large pour would allow more current (just like a wider trace), and would result in a larger solder blob. You probably need neither.

A simple trace between the middles of the pads might look like an accidental solder bridge if you don't know the circuit. To avoid such a misunderstanding, it might be a better idea to route the trace outside, if you can afford the space:

In general it's best not to pour over pads (without thermal reliefs). It makes them harder to solder and desolder. The exception is high current stuff or stuff where you are using the tracks as heatsinks.

Going directly between pads with a track can lead people to think there is a manufacturing fault, especially if the soldermask on the track flakes off. Still it may be the best option on a very cramped board.

Usually a U shaped track coming out from the chip as CL suggests is the way to go.

I have been known to put a U shaped track under the chip, the downside of that approach is you have no way of cutting the track if you discover a design flaw.