Gargoyle
Adventurer
Other things to consider.
Could you use material components while holding a two-handed weapon?
You must have a hand free to access a material component, but it can be the same hand that is used for the somatic component. So unless you rule that they can't hold a two-handed weapon with one hand while casting, then yes. Officially they haven't said whether you can carry (not attack with) a greatsword in one hand, but I don't think we really need them to tell us that. Of course you can carry it with one hand.
How about draw and then put away an arcane focus?
You can draw a sword as part of an attack, so I'd say you can draw an arcane focus as part of casting a spell. Sheathing a sword can also be done as part of an action, so you could put away an arcane focus as part of movement. Since there are no particular rules on this for arcane foci, and since we have clear rules on this for other items, I don't see a need for official clarification.
Divine casters are ok here as they can wear their focus rather than hold it. However they also have a number of touch spells. Surely you need a free hand for this or can you kick someone with a cure wounds spell?
t just says "make a melee attack", and has the range of touch, so I'd say this was a DM call, but it makes me smile to think of a kicking cleric. But most of the time, no; I don't think I'd treat this as an unarmed strike; it doesn't say to. I'd go with the assumption that it's just a touch with the hands delivering the spell, not a punch, kick, elbow strike, or head butt. An unarmed strike could be any of those things, but the delivery of touch spells should be through the hands unless otherwise specified, since the hand is what is needed to be free to cast the spell.
I don't think we will get a formal answer about any of this stuff. Some groups will hand wave all of this and others will like to emphasize the benefits of versatile weapons and component pouches over arcane focuses (in some cases)
I think people are overthinking a lot of these and that we really don't need formal answers about most of this stuff, just a little reading of the rules and common sense interpretation. Of course they invited this confusion by giving us options like arcane focus and not enough examples, so I don't think the questions are wrong to ask.