I am running Kubuntu 18.04. However, I have also tried loading Kubuntu 20.04 and 21.04 on different systems as well. All exhibit the same issue described below.
The indicator-kdeconnect app no longer allows contact updates via the Google API's. It seems that the Google "contacts.readonly" API has recently been retired (see [https://www.googleapis.com/auth/]). The newer Google "people" API is supposed to supercede "contacts". As near as I can tell, the "sms.py" module installed in /bin and /usr/bin contains provisions for dealing with both Google API's. However, any attempt to download my personal contacts into indicator-kdeconnect (i.e. ~/.local/share/indicator-kdeconnect/sms/contacts.json) only results a "Sync Starting" notification popup and my browser opening a window squawking about authorization errors ([https://accounts.google.com/signin/oauth/error?authError=Cg5kZWxldGVkX2NsaWVudBIdVGhlIE9BdXRoIGNsaWVudCB3YXMgZGVsZXRlZC4gkQM%3D&client_id=56930634232-sqama3feqgkq000m73db3mm4s6jch2c2.apps.googleusercontent.com]). It doesn't matter which browser is the default (Firefox or Chrome).
It should be noted that all other indicator-kdeconnect functions work. I can browse files on my cell, send/receive sms messages, et al without a problem. I simply cannot seem to authenticate properly to udpate the indicator's local contacts file.
It should also be noted that I cannot authenticate with Google via the SystemSettings app. I believe that may be a known issue but I do not know if this may be at all related to the indicator-kdeconnect issue I am experiencing.