I don't know why I couldn't find this information, or why this isn't more formally wrapped up in a Kasa app feature.

I changed the name of my WiFi network and had to connect my switches to the new one. After reading the docs, sites and watching a few videos, they all imply you have to set them up again. There were a few clues but nothing obvious. In fact, this official doc implies it is impossible: https://www.tp-link.com/ca/support/faq/2631 (bold is theirs):

Currently there is no setting on Kasa APP allowing us to switch to a different wireless network directly ... But if you want to connect to a different wireless network, you may change the wireless network by resetting your kasa device, and then follow the regular setup process.

Well this is how to do it...

I connected over 20 switches doing this. It takes around 1-2 minutes per device since you only have to enter the passord the first time.

First, ensure you are connected to your new wifi network before doing anything else or you may have to start over. I was using an iPhone but it should be the same (right?)

These two steps do not need to be done in any order:
 

1. Open the Kasa app. Also

2. Hold the left little button under the switch down until it first flashes green and amber. This takes about 5 seconds. Do not hold it down again for 10 seconds or you really will have to set it up from scratch as this does a full factory reset. If you do just the 5 seconds, the device will be ready to update (this is, not obvious at all when you see the next steps in the app, but this is what is going on...)

Now, in order:

3. In Kasa, tap the + button and choose to add a new device. Again, don't worry, you aren't actually adding a new device. This is just how you get going. Make sure you pick the right switch! If you don't it simply won't connect! It will seem like you have some sort of connection issue, but you do not. It is just not obvious that you picked the wrong switch type (e.g. if you pick a regular switch when you are working with a 3-way switch.

4. Follow the directions, telling the app that the device installed and then flashing green and amber, then connect to the device's temporary wifi network when asked. If you did #3 right, this will work just fine. Switch back to the app and let it think things through.

5. THIS IS THE MOST IMPORTANT PART. You will be asked if you want to reset the device. You want the less obvious button that does NOT reset the device. You will then be able to pick your wifi network and enter your new name and password and connect the device. 

6. YOU ARE NOW DONE! if you were to continue, the app would ask you to confirm the device name, etc, etc, etc, but ignore all that and simply close the app. You can then open it again and move on to the next device. That is right. As soon as your device connects, you are done. Nothing will change in the setup, or name or anything. The device will simply be functioning again, as before, but on your new network.

Note: do each device one at a time or it can get confusing trying to figure out which switch belongs to which temporary direct wifi network when you have to pick.

To TP-Link: Please just add a utility to update the wifi network for all devices. Other smart vendors have this feature. It should be trivial to tap, connect, pick the network and connect. Unfortunatly I figured this out on my second attempt. I accidentally did a factory reset on my first 3-way switch and now it stopped working unless the other side is ON (using a single 3-way switch for the setup). I'll start a new thread to ask for help on that one.