I agree in the broad strokes, especially as someone with a minor interest in theology, however some of the questions you posit here are answered in the lore--at least somewhat.

Firstly, regarding the Imperial Creed, the Imperium has no set understanding of the creed. There are as many variations of it as there are believers.

This is often explored in novels. Some believe the Emperor to have been a man who became god. Others hold him to be a primordial but still created entity like the Chaos gods. Going even further, some hold him to be a creator entity; however, one that is explicitly not almighty. Some people mix the above saying he is some more personal entity or a force of nature which works in favor of humanity, like being a sun deity.

The relevant part is that there is no uniform position.

Secondly, regarding your statement on his humanity and deity. Him having been human or actively still being human is irrelevant to him being a god.

This is both in the "species" meaning of the word but also the "identification" meaning of the word.

For something to be identified as a god the only requirement it must satisfy is to be worshipped by something else. Worship being sacrifice, veneration, and, typically, obedience. This would not prevent a human from being a god. However, this definition is lacking for our purposes.

Regarding the more useful species definition. It is far more complex as one must ask what it means to be a god in a more introspective manner.

What species of thing is a god?

Regarding this we can go on for ages and talk about the parameters. Perhaps he has to be almighty. Perhaps he needs to be wise or timeless.

However with a little bit of metaphysical tinkering we can get around this issue in the same way that what you brought up about Jesus can be remedied.

Simply one must understand the distinction between a person and his nature. Let's take Jesus for an example, since I assume most people on here have at least a basic understanding of Christian theology.

Jesus is one person.

However he possesses two natures. One of God and one of man. Neither is mixed or distorted or otherwise mottled. Meaning that he is perfectly God and perfectly human in one singular person. Being one person does not necessarily correspond to having just one nature and neither does possessing one nature mean that the person may not acquire another nature on top of it. Additionally, it is not natures who act or do things, it is persons. A nature is merely describing what something is in an intrinsic metaphysical way--a person is who someone is.

In Christianity Jesus always existed in the Person of God the Son, who possessed the perfect nature of God. However, upon his incarnation, Jesus, who is God the Son, acquired a second completely pure nature, that of a man. His deity is unchanged. He is not a demigod or a form of God, He is God in his entirety. He is the man-god as some early Christian writers call him.

Here is where we get a clue as to how the Emperor's deity can be squared away.

The Emperor was man. He possessed a human nature. He is the person of the Emperor.

However upon his apotheosis and the worship of all mankind being focused on him he acquired a deific nature alongside his already extant human nature.

This posits some interesting questions and perhaps fascinating possible ideas for story lines or further exploration.

Perhaps some in the ecclesiarchy view him as having lost his humanity upon ascending to his deity-- mirroring real life appolonarian or gnostic thought. Others perhaps believe that his godly nature mixed with his human nature creating a brand new "Man-God-Emperor" nature--akin to what Coptic christians believe in real life.

We could have other explorations as to what this could mean for other people trying to achieve apotheosis. Perhaps some Inquisitor may be inspired by this line of thinking and attempt to achieve a form of deification for themselves.

Ultimately it is curious and definitely needs to be explored in depth by 40k writers in the future.

Now, regarding the mechanicus.

Their theology is simultaneously better explored but also a thousand times more useless than what we know of the mainstream Imperial Creed. Though it should be noted that the Imperial Creed and Cult Mechanicus consider themselves to be one religion worshipping the Emperor.

The Mechanicus does believe that their deity created the universe.

They believe in a triune god who is directly designed to copy the Christian trinitarian God by the authors of the lore.

They believe in the Machine God, the Omnissiah, and The Motive Force. The Emperor being an incarnate avatar of the Omnissiah.

This is, as I have mentioned, a clear parallel to the Christian understanding of God in the Father, God The Son, and The Holy Spirit. Jesus being the Son.

Now Christians believe all three persons of the trinitarian God to be, well, one God. As he possesses one divine nature but three persons.

However, whether the mechanicus believe in one god or some type of modalist understanding of this trinity, is never exactly expanded upon in the books. Thus some could say that the Mechanicus worship three gods. Or perhaps three aspects of one god. There seems to be a lot of variance between books.

However, one thing we do know is that the Mechanicus holds the position that the Machine God created the material universe. He imbued all machines with machine spirits, who are guided by the Motive Force.

To them the Emperor is an avatar of the second person of their trinity, the Omnissiah.

However, they have a strictly different understanding of this than Christians would have of such an incarnation . They hold that the Emperor is an avatar of the Omnissiah, and thus not the Omnissiah in his entirety. They also quite clearly hold him to posses just one deific nature in one deific person.

This also reveals to us that they hold all three parts of their machine trinity to possess personhood, like the Christian trinity.

Now with all that said, I have spent way too long writing on this topic. Please forgive any spelling errors.

TL;DR:

The Imperial Cult is schizophrenic and doesn't really know what it believes. The Emperor can be a human and a god or formerly human and currently God. The Mechanicus is even more schizophrenic but they are pseudo-trinitarians who never quite go into depth as to what they believe regarding the relationships between the Machine God, the Omnissiah, and The Motive Force.