In the case of the Bitcoin node, you can use getchaintips RPC and it will tell you the current block height the node has processed. It also has a field for flags and at what block height they are activated; chances are if you aren't anywhere close to the Taproot flag block height then your node is not completely verified.

There is also a friendlier getblockchaininfo RPC that gives you the verification process as a decimal between 0 and 1 ( 1=fully verified).