In 5e, the rules state the following regarding spells with somatic and material components:

Somatic (S)

Spellcasting gestures might include a forceful
gesticulation or an intricate set of gestures. If a spell
requires a somatic component, the caster must have free
use of at least one hand to perform these gestures.

Material (M)

Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell. But if a cost is
indicated for a component, a character must have that specific component before he or she can cast the spell.

If a spell states that a material component is consumed by the spell, the caster must provide this component for each casting of the spell.

A spellcaster must have a hand free to access these
components, but it can be the same hand that he or she
uses to perform somatic components.

(5e Basic rules, p.79)

Now, I take this to mean that a hand holding a focus is considered free for the purpose of Somatic components, as the focus is serving as a replacement for the 'normal' components and the rule is in place that material & somatic components can use the same hand. I also assume this still applies even if the focus is a shield with a holy symbol inscribed on it, as is the case for Clerics and Paladins:

Holy Symbol.

A holy symbol is a representation of a god or pantheon. It might be an amulet depicting a
symbol representing a deity, the same symbol carefully engraved or inlaid as an emblem on a shield, or a tiny box holding a fragment of a sacred relic. The Player’s Handbook lists many gods in the multiverse and their typical symbols. A cleric or paladin can use a holy
symbol as a spellcasting focus, as described in chapter 10. To use the symbol in this way, the caster must hold it in hand, wear it visibly, or bear it on a shield.

(5e Basic rules, p.49)

However, I'm not 100% certain about that; The War Caster feat in the PHB (p.170) has a benefit of being able to perform the somatic components of spells even when you have weapons or a shield in one or both hands, and that's giving me a bit of doubt as to whether or not you can use a Holy Symbol shield to perform somatic components. That may be there just for if a non-Divine caster obtained a shield proficiency or if a divine caster was casting a no-material-component spell, however.

So, the question:

When using a focus or a component pouch, does the focus remove the requirement of the (uncosted) material components, or is the focus now the (sole) material component?

If the latter is true, then the rule of "A spellcaster must have a hand free to access these [material] components, but it can be the same hand that he or she uses to perform somatic components." extends to the focus, because it's no different from the material components that the spell normally specifies. It's literally just taking the place of the normal material components as a different material component. If it's the former, then the focus is an object that removes the need for material components, but it occupies a hand that cannot be used for somatic components as it itself is not a material component.

Given the specifc phrasing of the ruling of "A character can use a component pouch or a spellcasting focus (found in chapter 5) in place of the components specified for a spell.", I'm inclined to believe that the latter is true and the focus is acting as the material component in place of the normal components, but I am not sure.