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 ).
getblockchaininfo shows the latest block, and when I send a test transaction I can see it immediately in my mempool view by searching the txid. However if I then click on the associated address that's when I get the "Error loading address data" message.