Hi @Ollyk
Libraries can be a little confusing. Clear your head we’ll start from scratch.
Kicad supplied libraries are read only. If you wish to create, import or modify (even Kicad library parts) they must first be placed in Personal Libraries.
Two choices are offered for Personal Libraries: Global and Project.
Global Libraries can be accessed by any project at any time. They work like Kicad libraries: they are always available. These are located in a place (of your choosing) somewhere in your computer.
See this FAQ: KiCad 7 Beginners Guide to Personal Symbol and Footprint Libraries
Project Libraries can ONLY be accessed when the particular project they are tied to is opened. Project Libraries are located within the project to which they are assigned.
To create a Project Library, first open your project, and, in the case of a symbol library, open your Symbol Editor.
Next: select File > New Library > Project
You need to name the library (magenta arrow)
When you have saved, the library will appear in the list (red arrow)
The path to this library, (which can only be accessed when this project is open) shows in (green arrow).
You can confirm the existence of this library by going back to the library project (cyan arrow below).
The Project Footprint Library works exactly the same way, but you need to start proceedings the the Footprint Editor.
The library can be viewed and accessed on the LHS of your screen in both the Schematic and Symbol Editors in its alphabetical place amongst all the other libraries. (Yellow arrow below)
NOTE: this library will only show, and can only be accessed if this project is open.
Open a different project and that library will be absent.
Now you have a project Library.
If you want more libraries for this project, repeat the above process.
If you wish to change the nickname or remove the library from visible or active, go into Preferences > Manage Symbol Libraries > Project Libraries; but again, access to this is only while in the project to which the library/s are attached.
To place symbols in your new library, copy/paste, import, save as, or whatever else in suitable from the library containing the symbol/s you require.
Note: the screen grabs are taken from Linux Mint. Other OSs may show slightly different layouts and colors.