During the 1st part of the installation you are actually connected to the local wifi network generated by your HS200, same process as with the plugs and bulbs.  When you choose an network to bind your switch to, your phone will be disconnected from the default network as the switch configures to use the network you chose to bind it to.  This is likely why your phone is dropping the connecting.  The phone should revert back to your home network but if it doesn't just manually reconnect should fix the issue. 

@Jenson5 

This could actually be a resource limitation.  All routers on the market have tethoretical maximum for devices connecting.  for example for a baisic N300 router from us you can aniticipate 16 devices to be able to connect through DHCP and wireless.  On our standard routers the theoretical limit is 32 and on our premimum routers that number is 64 per band.  This should be pretty common throughout all manufactures.  With this many Smart devices plus what ever other devices you have working on 2.4GHz you could simply be taxing the capablities of your router.  The best way to test is to remove a few devices temporarliy, power cycle to clear the DHCP lease times and then try to reconnect this switch.  If it works then you will know it is a resource issue.  If you have devices that can operate on either 2..4 or 5 we would recommend shifting those devices to 5Ghz.  If this is not possible a more powerfull router would be recommended.  

For TP-Link The Deco M5, P7 or M9 is a greate choice.  The M5 and M9 both also now feature Kasa intergration so you can control you Kasa Devices through the Deco App.

For a more traditional router,  The Archer C5400X or AX6000 would be your best bet. 

Best Regards 

@Jenson5 

I did a quick search for this and found a KB article on netgear's site that stated NETGEAR home routers can accommodate up to 32 clients per wireless band. If your router is dual band, the total wireless clients your router can handle is 64.  So it does look like you may have a resource issue.  Before spending the money on a new router to accomidate all your device needs I would recommend contacting them to see if there is anything that can be done to expand the device coverage.