Well, I think Scratch's users should have their own sprite / costume library, in which, they could keep their own sprites and costumes.
Well, how it would look like?
I think it would look like this:
User's own library could be accessed by clicking the “My Library” category on the Sprite Library:

The same with the costume library:

User's own library could look like this:

While user's own costume library could look like this:

To add a sprite into their own sprite library, they could right-click their wanted sprite, select Add, and it would be added, just like in this mockup:

The same would be with the costume library:

The user could remove their own sprite/costume by just clicking the delete button:

Mockups made with paint.net
Sound Library
As suggested by @Sunarcher, the mockups for sound library have been made.
Like sprite and costume libraries, the your own sound library could be accessed in “My Library” category:

User's own sound library would look like this:

To add a sound into their sound library, the user could just right-click and select Add, just like with sprites/costumes:

To remove the wanted sound, the user just could right-click the sound in their sound library, and select Delete:

Mockups here also made with paint.net
Backdrop Library
As suggested by @elephanttime, the mockups for the Backdrop Library have been finally made.
Like sprite/costume/sound libraries, you could access your own sound library in “My Library” category:

This is how user's own backdrop library could look like:

To add a backdrop into their backdrop library, the user could just right-click and select Add, just like with sprites/costumes/audio:

To remove the wanted backdrop, the user just could right-click the backdrop in their backdrop library, and select Delete:

Mockups here also also made with paint.net
Minor ideas
There are some minor ideas, suggested by Scratchers.
Nambaseking01's ideas:

• If a user adds a sprite/audio with the same title as another one, it would get that title but then with a number behind it. For example, if there is a sprite called “fun”, and another sprite called fun was added into the library, it would be called “fun2” automatically, and if there was another one, it would be “fun3”, and so on…
  
  
• The Scratch Team should be able to view anything in your sprite/audio library, and maybe one will think “Oh no! The Scratch Team will see all my private audios and sprites!”, but here's what they said about a suggestion that the Scratch Team shouldn't be able to view unshared projects. The same reasons are applicable for this library.
  
  
• If there was a sprite/audio that looked/sounded exactly the same as another one, there would be an error message saying “This sprite/audio already exists in your library!” and you wouldn't be able to add it just to prevent server space clogging.

Why would Scratch need this?
Why? There are some answers why.
1. Easier for animators
Some animators could have a lot of characters, but they also could have a backpack, full of many resources. This would be easier for them to manage, instead of searching through the entire backpack.
2. Easier for everyone
This could be easier and could change Scratch forever. People, who want to remix an AY project, they can find their wanted character easily, instead through searching their messy backpacks.
Some people can have many SFX in their backpack, and sound libraries can make their management 100% easier.
This would make Scratch easier; what's even the point of backpacks, if custom libraries exist?
But, also, there is one more important thing about my suggestion. They would be private: other users couldn't find and use other person's library.
And now…
Thank you for reading my entire post. It took me half an hour to make these mockups and write ALL of this.
Now, write your opinion below!

Support.
I hate searching through my backpack all the time.
(Although, I think this might be a dupe )

Support! I have a lot of sprites in some animations I am planning on making, and this would help. This is a lot better than the backpack.

I like this idea! Would be very useful for series, as typically, a character would be used repeatedly. While I only use the backpack for music, this would still be very beneficial.

Thank you for your feedback! I like how 3 people like my idea.

Support. I truly don't like having to dig through my backpack, and my backpack doesn't even have that much stuff in it, its just my OC and a ton of sound effects and other stuff. Maybe add a sound library too?

Support! Technically everyone can just make their own “sprite” folder on their device, and I have one of those, but I have never actually used it. Could be quite useful, especially when you are making animations and you want the same character!

Giga404 wrote:

Thank you for your feedback! I like how 3 people like my idea.

[offtopic] I think that's your 100th post! Congrats! [/offtopic]

Vercte wrote:

Giga404 wrote:

Thank you for your feedback! I like how 3 people like my idea.

[offtopic] I think that's your 100th post! Congrats! [/offtopic]

Thanks for congratulating me!

Mega support! I've never liked how you can't sort your backpack by type, and this would help.

Support! I would actually use a “My Library” for the sounds tab a lot more, because the music in my computer is all over the place. I could also see this beneficial for Scratchers who repeat sprites and have a backpack that's full of stuff and tiring to look through.

I can't thank you enough for suggesting this! MEGA SUPPORT!!! This is useful for anyone with an overflowing backpack!

backpack bad custom library good

anyways i think it should be a library where all scratchers share it like a sprite archive, support but needs modifying

WAIT PURPLE CAT OH NO-

ittybitmap wrote:

backpack bad custom library good

anyways i think it should be a library where all scratchers share it like a sprite archive, support but needs modifying

WAIT PURPLE CAT OH NO-

It seems like you got the joke! The purple cat is actually a reference to the man behind the slaughter meme.

Support. So backpack would only be for scripts then?

So… it's the backpack?

Mr_PenguinAlex wrote:

Cool idea, but… isn't this what the backpack is for?

I guess this would be kind of a replacement for the backpack:

Maximouse wrote:

So backpack would only be for scripts then?

Maximouse wrote:

Mr_PenguinAlex wrote:

Cool idea, but… isn't this what the backpack is for?

I guess this would be kind of a replacement for the backpack:

Maximouse wrote:

So backpack would only be for scripts then?

The backpack should only be for scripts… I have never used it once for sprites

PizzaAddict4Life wrote:

The backpack should only be for scripts… I have never used it once for sprites

I have quite a few sprites in mine
But if this gets implemented, all sprites in the backpack should probably be automatically moved to your sprite library. Same for costumes and sounds.

Maximouse wrote:

PizzaAddict4Life wrote:

The backpack should only be for scripts… I have never used it once for sprites

I have quite a few sprites in mine
But if this gets implemented, all sprites in the backpack should probably be automatically moved to your sprite library. Same for costumes and sounds.

What about the code in the backpacked sprites?