According to lead rules designer Jeremy Crawford:
The intent is that the shield hand can be used for a somatic component if the holy shield is used to cast the spell.
In a tweet exchange on 21-23 November 2014, @Sword_of_Spirit asked:
@JeremyECrawford Holy symbol engraved shield counts as material component, but does holding the shield replace somatic component also?
Crawford replied:
@Sword_of_Spirit The intent is that the shield hand can be used for a somatic component if the holy shield is used to cast the spell.
And further clarified that the shield arm cannot be restrained:
@Sword_of_Spirit You still need use of the shield arm to move it while performing the somatic component.
Absolutely Not
As others have stated, no you can not use a focus (of any kind) while Wild Shaped, even if the animal you morph into has hands, and they are empty and holding the focus. All of the information you posted in the original question provides the answers for you so long as you cross reference them. But a lot of people have missed a crucial part of why it can't be done.
The description of the Druidic Focus says (5e PHB, p. 151):
A druidic focus might be [...] a totem object incorporating feathers,
fur, bones, and teeth from sacred animals. A druid can use such an
object as a spellcasting focus.
This essentially states that you get to create a focus out of whatever you deem worthy to call a focus; pretty neat.
The description of Material (M) components says:
Casting some spells requires particular objects, specified in
parentheses in the component entry. A character can use [...] a
spellcasting focus in place of the components specified for a
spell [but not costly or consumed components]
This is the start of the unravel. Here it says you can use a focus instead of a material component (so long as it has no cost/isn't consumed). So essentially focuses are just fluff/filler for material components that most people over look anyway, but if you don't overlook that stuff it's still a pretty minimal net gain.
Part of the description of the druid's Wild Shape feature says (5e PHB, p. 67):
- You choose whether your equipment falls to the ground in your
space, merges into your new form, or is worn by it. [...]
This portion infers that you get to wear or hold your focus if you so choose when you Wild Shape, which is pretty cool.
The druid's Beast Spells feature says (5e PHB, p. 67):
Beginning at 18th level, you can cast many of your druid spells in any
shape you assume using Wild Shape. You can perform the somatic and
verbal components of a druid spell while in a beast shape, but you
aren't able to provide material components.
This is the crucial spot. It specifically says no material components. If you recall from what exactly a focus is, it is essentially a fancy material component. Meaning it can't be used, not because you can't "hold" it, but because for Game Design purposes they disallowed it.
This is further backed up by the fact that they allow somatic components (hand and body gestures) even if you don't have hands or the appropriate body part to do the somatic component, i.e. a snake making a hand sign. So holding/wearing the material component/focus is irrelevant because it is completely outlawed in RAW.
The druid's Archdruid capstone feature says (emphasis mine):
At 20th level, you can use your Wild Shape an unlimited number of
times.
Additionally, you can ignore the verbal and somatic components of your
druid spells, as well as any material components that lack a cost
and aren't consumed by a spell. You gain this benefit in both your
natural shape and your beast shape from Wild Shape.
Doesn't this seem a bit redundant? It is because it is trying to show you that it is essentially an improvement to Beast Spells. At this point, once you reach 20th level you no longer need the material/focus component. So even at level 20 the answer is still technically no, but it becomes irrelevant because materials/focuses are no longer even needed.
However, this is D&D - so if the DM says, "Well that's stupid, you should be able to use your focus as long as you are wearing/holding it"... Then boom, there you go: the true answer is "yes, you can, so long as your DM handwaves it".
Best Answer
Generally taken that you can't, not a problem for Artificers as all their spells have M
You're right that there's no provision for using a spellcasting focus on spells without a material component. As the rules are generally taken as defined positively (ie. describing what you can do, as opposed to what you can't do), this is often taken to mean you can't use a spellcasting focus if the spell doesn't have a material component. This leads to some amount of dancing around getting a hand free, but (in my experience and as a DM) a lot of tables don't care too much about components unless it's actually interesting in the situation (silence, underwater, etc.).
When it comes to specific magic items, which is where getting to use focus on non-M spells starts really being a boon, it is worth noting that a number of magic items, eg. the Arcane Grimoire from Tasha's, boosts the DC from it being held, independently of whether you use it as a focus.
And specifically for Artificers, this is simplified because of the specifics of their spellcasting feature. Artificers cast all their spells through their spellcasting focus, even if their normally don't have a material component (note that the clarifying parenthesis was added with the Tasha's printing):
Feature's such as Arcane Firearm expand what you can use as a spellcasting focus (creating an exception to the general rule), you still need to use a focus, meaning it has an M component. (As a wand is not a tool, you presumably don't need to have the non-existent wand proficiency, as the feature wouldn't work if you had.)