If I am holding a shield and sword, do I need the Improved Pact Weapon eldritch invocation to cast spells with a material component?

Question

I am playing a Hexblade, who is holding a shield in one hand, and a sword in the other.

Because I don't really want to use a bow, and like a lot of other invocations, I have decided not to take improved pact weapon.
To make gestures for the somatic components, I can stow my sword as a free object interaction, and then cast the spell. (and draw the sword again in the next round)

Is the same also possible for spells with a material component? I have a component pouch on my belt. Does using my component pouch require a free object interaction? Does the cost of the component affect this in any way?

I have found the following tweets by Jeremy Crawford on the subject:
Link 1
Link 2

To me, it seems, as though they are contradicting...
Do I need improved pact weapon, to use spells with a material component, if I also want to use a shield?

Answer 1

You can empty your hand before casting

Retrieving your component pouch in order to perform the material component of the spell may require object interaction (if in a pocket), or even an action (if in your backpack). Instead, a component pouch is normally kept on your belt where you can access it easily.

You only need a free hand ready to manipulate your component pouch as part of 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 a spell's material components -- or to hold a spellcasting focus -- but it can be the same hand that he or she uses to perform somatic components.

When a spell describes how material components are handled or used, that handling/use takes place as part of casting the spell, it does not require a separate action.

Note that you do not have to sheath your sword unless totally necessary. You can simply drop it and keep it propped up against yourself or held with your shield arm. However, another enemy could try and grab it or kick it away, so make sure you are careful.

Answer 2

If you don't want to release your weapon, yes

As you rightly determined, in order to handle somatic components, you need to either drop or stow your weapon to free your hand. And the same logic applies to material components.

If a spell requires a material component (PHB, 203):

A spellcaster must have a hand free to access a spell's material components -- or to hold a spellcasting focus -- but it can be the same hand that he or she uses to perform somatic components.

Using a component pouch vs a spellcasting doesn't change the calculus. Both need to be accessed by a free hand.

Do note that you can use the same hand for both somatic and material components (you don't need two free hands, just one):

To close the loops, it as you thought: you have one hand holding a sword and another hand equipping a shield.

That leaves you with zero available hands. Which means no material or somatic component access and no spellcasting for those component required spells.

Unless you have an ability, such as the improved pact weapon invocation from Xanathar's Guide to Everything, you must meet the requirement of a free hand.

You can still meet this requirement, but for a cost

However, you can still create a free hand on your turn in order to cast a spell with a material component.

You can either drop your weapon or sheathe your weapon and then cast your spell.

The downside to this is that you no longer are wielding a weapon. This is important for things like opportunity attacks as well as any other mechanics, like that require you to be holding your weapon. And if you're wielding a sword a shield, odds are you are in melee combat. Of course, if you drop it, it is also at risk for being picked up or moved by an enemy.

The case of costly or consumed components

For these, a focus doesn't matter. You need to have these components on-hand and accessible to touch. If you've got a component pouch, that should do it. Otherwise, just a pouch with those components hanging near it is identical. But you can't use a focus for these, you need the actual components.