I use a paid tier of Contacts+ https://www.contactsplus.com/
It syncs well with Google, Office 365 and iCloud, can pull info from Twitter. Unfortunately LinkedIn made changes that blocked a full sync though you can periodically download and import your LinkedIn contacts. Oh and you can scan business cards if anyone still gives you those.
I don’t do anything very sophisticated beyond tagging contacts as personal, work and work alumni, friends, family or with a specific conference where I met someone but there’s plenty of built in and custom fields to let you do more.
The important thing for me is all my contacts are available everywhere including my current company’s Outlook, and in my iphone natively via iCloud sync. I often prefer the Google Contacts UI for batch tagging. And I can use Google or Microsoft duplicate detection in addition to Contact+ flagging dupes and changes and it all stays in sync. There’s a native app for my phone and my Mac too.
I haven’t personally used Google Contact labels, but there are two awesome iOS/macOS contacts apps that may help. Contacts+ (web app/iOS app) can sync your iOS/macOS address book and Google Contacts (even multiple accounts) so they are always identical. It can even scan email signatures for updates to your contacts, if you’re ok with that function privacy-wise. The other is CardHop, by the same dev as Fantastical (an awesome and powerful Calendar app). CardHop is like the Address Book on steroids and probably has what you’re looking for.
If you don’t mind using one more cloud service, https://www.contactsplus.com/ (you’ll maybe need a trial or to buy one month, but I suspect you could use the free tier to sync to Google, remove the sync, then sync with iCloud).
Full disclosure, I used them previously under the FullContact name, but removed all of my data from them when I de-googled some moons ago. My experience is therefore out of date.