You can find the symbols panel in Affinity Designer via the view menu and studio and symbols command.
Open the application and then View menu and then Studio etc. The panel has three buttons, create and detach and sync. They can be anything, designs such as cogs, squares, text, multiple path designs, lines, multiple text, etc
Select a path / shape / type and go to the panel and click the create button. If you have one path then the create button will add that single path (such as the cog design above) to the panel. If you have multiple shapes selected then you will add multiple presets. See the groups section to get around this but of course, you maybe happy to have multiple presets created
If you want the paths to be all added together then you must first use the layer menu and group command. Click create after grouping the paths. Select multiple paths and layer menu and group command and symbols panel and click the create button
Drag the presets from the panel and repeat for the number of copies you wish to create and re-size, re-position, rotate etc the artwork. It is super easy to add them to the document and once added, they can be duplicated and then edited etc as required
Select an instance and click the detach button and edit the paths as normal. If you wish to add it, click the create button. Once it has been detached, you will see the entry in the layers panel has changed and any changes you make to the path now will not change any of the instances or in the panel itself. As soon as you re-create it then any changes will be reflected in the panel.
Select an instance and drag the design to the art board and go to the layer panel and expand the layer panel. You will see a single path or multiple paths. To change one of those paths and the preset in the panel will also be changed as will any of the artwork instances. You can manipulate the design in all kinds of ways such as re-coloring the enclosed artwork as well as scaling it and rotating it and re-positioning as well as adding layer effects etc to the design and again all of this will be reflected in all the other instances. Click the path you wish to change and apply layer effects or change the color to a solid color or gradient or perhaps round the corners using the corner tool or and shift or scale the path or rotate the path. You can also repeat the same with other paths in the group of paths. Any change to the paths will be reflected in a change to all the copies and the panel
You can edit the artwork and add new paths etc. It is probably easiest to edit it by working on just one design in your document. If you try and work on multiple instances it can become a little complex. Any addition of new paths in the edited item, will be reflected in all of them.
Go to one of the instances in the layers panel and select, expand it out and then go to the path you want to delete. Select it and delete and then all the other instances will also update and the update should also happen in the panel also.
You should note that the presets are not permanent, they are only for the document. There appears to be no way with the current version to save them for permanent use in other artwork files. Of course, you can always copy and paste the presets from document to another document.
You can right click any of the items in the panel and delete them as well as rename them.