This must have happened because your coins from 2010 are locked in P2PK (pay-to-public-key) script which doesn't have an address.
So, by importing only the address, you'll only be able to see those new coins in P2PKH (with the address start with '1').
If you want to scan your coins from 2010 properly, import its public key.

You can use Bitcoin Core in offline and online machines to create a cold-storage set-up for safety reasons:
[Offline Machine]

• Open Bitcoin Core, create a New wallet with "File->Create Wallet..."
• Tick the options "Make Blank Wallet", "Descriptor Wallet", (enable encryption if you want) and create the wallet
• Open the console, make sure the wallet's name is selected in the console's "Wallet:" drop-down menu
• Type the command: getdescriptorinfo "pk(YOUR_WIF_PRIVATE_KEY)" and take note of the "checksum" which looks like this "#2ny75tj9".
  Replace "YOUR_WIF_PRIVATE_KEY" with your private key, since it's offline, doing so should be relatively safe.
• Type the command: importdescriptors "[{\"desc\": \"pk(YOUR_WIF_PRIVATE_KEY)#CHECKSUM\",\"timestamp\": 0\"}]"
• After that, the offline machine should now able to sign transactions that you'll create in the online machine.
• Now, to get the public key that you need to set-up the watching-only wallet in your online machine, type: listdescriptors
• Take note of the "pk" descriptor in the result, it should the the same as the one you've imported but has PubKey instead of PrvKey.
  
  

[Online Machine]

• Open Bitcoin Core, create a New wallet with "File->Create Wallet..."
• Tick the options "Disable Private Keys", "Make Blank Wallet", "Descriptor Wallet", (enable encryption if you want) and create the wallet
• Open the console, make sure the wallet's name is selected in the console's "Wallet:" drop-down menu
• Type the command: importdescriptors "[{\"desc\": \"pk(YOUR_PUBLIC_KEY)#CHECKSUM\",\"timestamp\": 0\"}]"
  It's the pk descriptor from "listdescriptors" command in the steps above.
• After it finished rescanning, the funds should now displayed excluding the 6 early dust transactions.

[To Create Transactions]

• Create an Unsigned transaction in the send tab of the watching-only wallet, save it in your flash drive or other methods of offline file transfer.
  Note: you might need to provide a "Custom change address" if you're not sending the entire amount since you don't have one. (or just "Use available balance")
• Import it to the offline machine via "File->Load PSBT from file...", Sign it, export the signed raw transaction just like what you did above.
• Import the Signed raw transaction to Watching only copy and click broadcast to send it.
  
  

For the blockexplorer result:
Most blockexplorers tend to correlated transactions with P2PK outputs to its P2PKH counterparts by deriving an address from that public key.
But it's not the proper way to show them, P2PK outputs should be searched in a blockexplorer by its TXID.[/list]