No, Jesus is not 'fully God'. He is like God, having His fullness and His image and His form. None of which make him God.
Jesus spoke truth when he said,
Now this is eternal life, that they may know You, the only true God, and Jesus Christ, whom You have sent. John 17:3
Jesus was in no doubt who God was - and it wasn't him. Being the son of God is not God - there were many 'sons of God'. Jesus is the only one who is without sin. No one else was in any doubt who God was. The disciples, Apostles and the whole NT is consistent in having only one God - the Father. His son Jesus is not that God.
I am the way, and the truth, and the life John 14:6
Jesus is the way to what? The Father. He speaks what? The truth about, and of, the Father. What is the life? The life of the Father that he would have after his resurrection - certainly not before as he was mortal, and that man could also have.
Making up 'truth' from inferences and speculations that doesn't fit with the rest of the biblical text is poor practise. Some like to infer that Jesus (the Son) and the Father are equal yet not one verse supports it.
Or like, 'In the beginning was the Word', 'Jesus is the Word', SO, Jesus MUST be 'in the beginning'! It's nonsensical and ignores the whole NT.
The "Logos/Word" is a person.
Yes - but only when the 'word' became flesh. When was that? When he was born ~2000 yrs ago.
If Jesus was the 'word/God' in the beginning (whenever that was) then death would never be master over him.
Romans 6:9 knowing that Christ, having been raised from the dead, is
never to die again; death no longer is master over Him.
As noted in a comment below by Nigel, "The death of Christ was a matter of humanity. Sin was eradicated in his death. But he, himself, did not die."
What? God didn't send His only son to die for our sins? It was just a charade!? Perfect example of making stuff up!
That is why we have many bibles inserting 'begotten' in John 3:16.
For God so loved the world, that he gave his only begotten son, that whosoever believeth in him should not perish, but have everlasting life.
This way they can have an 'eternal Son' who is not mentioned anywhere from Gen to Rev, AND a human son who could die and be tempted etc.
God has only one unique son and making him begotten when the text has none of it is a shifty process and has continued the deception begun after the Apostles.
Looking at the last verse of John 14
But that the world may know that I love the Father, and as the Father has commanded Me, thus I do.
We see that Jesus is certainly not 'equal', but God's servant - unto death.
So the OP's premise that - "the Word is Jesus by implication who is therefore God", is absurd and irrational - not to mention totally unbiblical. When we allow the text to interpret itself, and not imagine strange constructs, we get closer to the truth Jesus brought.