@Rand 

Were there any recent changes to your network beside putting in the new router?  At the time you setup the new router did you use new network credentials or copy the existing ones?  Did you try to change the credentials when the issue began?  Are you using any special features like Smart connect on your network?  Any changes to security or encryption types?

@Rand 

Did you reuse your old network credentials when switching to the new router.  While in most cases that shouldn't be a problem at times it can be and the devices will need to be reconfigured.  I personally had to do this when switching from one of our older routers to a new one.  Even though my SSID and Password were the same all of my Kasa Devices 5 bulbs, 2 cameras and 1 switch needed to be factory reset and reconfigured to connect to the network again.  You mentioned you reconnected them but was it by factory resetting and reconfiguring?  Also prior to the devices disconnecting did you make any changes to the network like enable a different encryption like WPA3? 

Another possiblity is that most people don't know this but a network has limits of how many devices can connect to a band.  This is outside the subnet or DHCP pool limits.  For TP-Link its is in most cases 32 or 64 devices per band.  I don't know what Netgear's are but since we all use similar chipsets to control our routers its likely around the same.  You can try to enable your guest network and put the Kasa devices there and see if they are stable.  If so that is likely what the case was.