The implanted chip doesn't even have to be writable, or contain any information at all except the person's unique ID number. Any data associated with that ID can be stored on -- and instantly retrieved from -- any number of databases.
The chip could be as simple as those low frequency RFID chips that veterinarians have been implanting in pet cats and dogs for many years. These chips contain only a unique ID number. Implantation is subdermal by means of a syringe, and takes only a few seconds. No incision.
For humans, the implanted chip is functionally equivalent to a fingerprint. But a chip reader is considerably cheaper and more reliable than a fingerprint reader (no ambiguity). And matching a number is far easier than matching a fingerprint (no ambiguity with a number). And the chip can be read from several inches away -- through gloves and such -- whereas a comparatively low cost fingerprint reader requires direct or almost direct contact. (Longer range fingerprint readers are available, but more expensive.) Gov could read an implanted chip surreptitiously much more easily than a fingerprint.
Another way of thinking about the chip is like a driver's license. A cop runs your license number and gets back your personal data, driving record, outstanding warrants, insurrectionist risk level, etc. Whatever info gov has you, the armed government worker gets just by having your number.
Edit: And linking your checking account (or equivalent) to that number would be trivial. So one-stop vax checking and shopping. Or not. Sorry, you've reached your meat limit for this month. Sorry, you've reached your lifetime ammo limit. Sorry, you made a mean post online -- no alcohol or chocolate for 3 months. Sorry, you missed your mandatory re-education session yesterday -- stand by for transport.