The existence of god, however, is a metaphysical claim.
The first statement is simply putting forward a definition.
Similar to "wormholes can instantly transfer you from one point in the universe to another". We're just defining the term, whether wormholes / god actually exist, is a different question.
It's a bit more complex than that. You could say "god is omniscient" is a proposition in logic but you need some axioms first. "God as defined in the Bible" might be a good start (although not too easy as Bible is self-contradictory in many places and doesn't provide a clear definition of God).
The God of the Bible offers a profound reply to the question "Who are You?" He replies "I AM that I AM" as if He is not readily definable.
There are many characteristics of this God that spelled out in detail; His desire for truth and justice, His love for the widow and orphan, His hatred of evil and injustice, His power and glory, and His plan for this world. So even if His whole is blurry, there are aspects of His character and abilities that are spelled out in detail.
Is it enough for a metaphysical debate? I have no idea.
I can think of counter examples to the attributes you gave earlier, but if you've read the texts and have not found them yourself, it is unlikely any logical or philosophical analysis would be persuasive.
Its not, though.
> The first statement is simply putting forward a definition.
Any coherent discussion (metaphysical just as much as scientific) needs shared definitions; merely stating a definition doesn't make a statement scientific.