The previous answers are a bit ridiculous. You would NOT need to get a Pi Pico 'recertified' if you modded it to allow the use of an external antenna. You can swap external antennas on your wifi hotspot or router, you can add a 'cantenna' or yagi to your router or the wifi card in your laptop. As long as you don't amplify the signal electronically over the FCC limits (see https://www.air802.com/fcc-rules-and-regulations.html) you would be hard pressed to exceed allowable EIRP. A 3db gain antenna is certainly not going to be a problem when added to the Pico with its max radio transmission wattage of around 125mw.
Replacing the onboard antenna by cutting the feed trace and soldering on a coax connector would require some fine soldering skills. They are very tiny, very fiddly, and the plastic melts VERY easily (https://www.digikey.com/en/products/detail/te-connectivity-amp-connectors/1909763-1/4729711). I would advise just cutting the u.FL connector off the end of the cable of your new antenna, stripping it back 1/8" or so, and soldering the center and shield directly to the feed and ground on the board, as close as possible to the radio chip. to the board. Also, this will disable to onboard antenna.
Changing only the antenna just dictates the shape of the transmission pattern. With higher gain antennas the signal will be more directional (stronger transmission and more sensitive receive in some directions, less in others). The total radiated power will be the same. So, pay attention to antenna placement for best effect.