Is blockchain stateless and UTXO stateful?

To my knowledge, when a new node joins a network, it downloads over 500 GB blockchain data used to verify the integrity of the blockchain.

Blockchains are difficult to rewrite but easy to check, so start by checking the headers from genesis blocks to chip blocks, regardless of whether the downloaded blockchain is corrupted or not.

Then repeat the body of the block from Genesis block to Chip block that takes days or weeks to build UTXO (the current balance of each address).

For all blocks in iteration:

• If it is the output (destination) of a transaction, add the address to the UTXO set.
• If it is the input (source) of a transaction, remove the address from the UTXO set.

So can we say that the blockchain itself is stateless? This is because it only stores transaction history, as additional operations allow only new blocks.

From that stateless data, all nodes can construct a UTXO set, where all nodes hold their state in internal memory (the same way as the way Mempool was saved). correct?

If correct, it may be that all nodes have different utxo.

Please clarify my understanding.