The Sword Spirit was likely correct. Before its death, it was indeed close to becoming a Half-step Golden Immortal. He could feel the immense power gap between them.
However, he was not without advantages.
The Sword Spirit was, after all, just a Sword Spirit. It had to rely on the power of the Purple Dawn Sword. Previously, the Purple Dawn Sword had no owner. He didn't know whether something happened to this sword, or if some True Monarch Purple Sun knew they were going to die, or for some other reason, wiped the aura of this Purple Dawn Sword.
Without an owner, after he used the Blood Coagulating Stone, he naturally became half the owner of this Purple Dawn Sword. However, the Sword Spirit constantly prevents his aura from fully entering the sword, so the Purple Dawn Sword has not fully acknowledged him yet.
Even so, the Purple Dawn Sword tends to accept his aura, so the Sword Spirit cannot fully borrow the aura of the Purple Dawn Sword.
