So, the three points of contention here are
- what is meant by 'carried'?
- what is meant by 'readied'?
- what is meant by 'set against a charge'?
The first one is a common point of contention. Many items confer their benefit upon their 'bearer', 'possessor', or even worse 'owner'. It is generally clear that wielded/worn is a more stringent requirement than any of these, but the exact interpretation of each of these and how they each differ from the other is a subject of intense consternation. Obviously, whatever you decide 'carried' means in one context should apply to other contexts, but beyond that there's not much to dicuss in terms of the rules, as written.
In English lugging something around in your backpack is certainly 'carrying' it, but e.g. loading it into a wagon and driving a team of oxen from your comfy front seat is disputable. We can say "Mule team 6 carried the shipment to Freeport", but even if you're the head of Mule team 6, far less people would agree that you had carried it. Still, it's not uncommon for management in such situations to refer to your activities that way: "Hey, Bob's Team has a busted axle, they need a mechanic, can you have John carry some parts over on his way to Neverwinter?".
In conclusion, backpacks are pretty safe, but the exact limits are something you're going to have to decide on your own.
Now, having a readied action and being able to use it are not the same thing! Or rather, they are possibly not the same thing! See, nothing stops you from taking actions after you ready an action and before it triggers, even normally.
So, for example, you could ready an action to stab the next person who enters the room with your dagger, then drop your dagger and draw your halberd using Quick Draw (both are free actions). When someone charges through the room, you get an AoO with the halberd, and then stab them with the dagger that you dropped when they close. The RAW make no accomodation for the possibility that your ready action might no longer be viable due to changing circumstances when your trigger is met. Even if you can't take actions, someone else might disarm your weapon in the above example, or otherwise do something that seems like it would negate your readied action but does not actually do so.
The reason I bring this up is that the situation where your greatsword is in your backpack when your readied action involving it triggers is not unusual. It's just another example of the really-common problem where somebody readies an action, somebody else tries to stop them from being able to take that readied action before it's triggered, and then the rules seem to say they can take the action anyways, even though they are no longer eligible, because they were eligible at the time they readied it. If/when you house rule this odd behaviour away, the backpack thing should be similarly affected. And if you don't houserule it, someone could, while hidden, ready an action to halberd the next person who charges them, drop the halberd and move action over into plain sight, and then take that action when the enemy charges the apparently unarmed character, dealing double damage on a hit. So stabbing people with a sword they're at least carrying is hardly weird by comparison.
On page 160 of the PHB the Ready action is described. It's weird. The rules specifically call it out as its own sort of action, completely separate from the standard and move action types: it's a 'Special Initiative Action', like the delay action. However, readying is also a standard action, according to readying's own text on that page. So... that's weird.
Anyways, the important thing here is the section about readying against a charge. That's a specific kind of ready action, just like drawing or sheathing a weapon is a special kind of move action. So this item doesn't give you a ready action, but rather the results of this specific subset of readied action (though that ends up being mechanically equivalent as far as I can tell).
The worst part of this (in fact, the only really problematic part of this) is that all ready actions are, as previously mentioned, 'special initiative actions'. By the rules as written, every time you use these boots your initiative probably changes. That's not particularly helpful in terms of your combat options, most of the time, and basically means you end up skipping your next turn, which sucks. Much more importantly, people changing initiative counts mid combat can be a real pain for some group's logistics. You may want to consider house ruling the item to not change your initiative.
Set against a charge
This is synonymous with 'readied' in this context. Weapons with the 'brace' special property can be set against a charge as a ready action, which then lets them deal double damage. This and the last thing are talking about the same thing.