Just a warning upfront - I'm an engineer, but not an RF engineer, so I do see some things, but I'm almost guaranteed to miss others.
As far as your highlighted line, it is a trace, but not a via. A via connects the trace on one plane of copper with a trace on another plane.
That trace should really be as short and direct as possible. Wrapping around the back of the module and along other signal lines is not a good idea. I see that the closest line to it is 3.3V power, so that acts basically as ground for small signal, but any power spike is bound to couple into the antenna line as well, at least some. If possible, it would be best to have ground on both sides of the antenna trace on that side of the board, as well as the whole surface on the other side of the board from it. Might also want to guard it by having vias connect the ground planes on either side of it to make kind of a 3d cage around it.
Additionally, you should try for 50 ohm trace impedance on the antenna line. However, there is no one-size-fits-all answer for the width of this line. It depends on the exact board parameters, and even to a small amount on the frequency of the signal. There are trace width impedance calculators that you can use to get this answer. https://resources.pcb.cadence.com/blog/2019-just-how-wide-should-a-pcb-50-ohm-trace-width-be
Almost guaranteed that it's correct to ground those 4 outer pins of the antenna connector. View the datasheet of the specific connector you are using to be 100% sure.