Uploading Photos - Can't Access Photos Library

Direct answer to your question:

Create an Album in Photos with all the photos you want to print, then select it and chose File > Export > Export Album. On the next screen select the options, then click on Export. The following screen is to choose where you want to save it - choose Desktop. Now the folder full of your images is easily accessible.

However...

I would feel a lot better if you contacted the printer for detailed instructions. This all seems way too complicated for what it should be.

What are you trying to print? Individual photos? Photo books? Calendars?

Did you try software apps such as Mimeo or Motif? They automate the entire process. The apps themselves are free.

https://apps.apple.com/us/app/mimeo-photos/id1282504627?mt=12

https://apps.apple.com/us/app/motif-photobook-album-maker/id1404636482?mt=12

The usual way to access photos from your Photos Library by other applications id the Media Browser.

When you use the image browser in any application or the "File > Open" dialog, you can access the Photos Library from the file chooser dialog in the "Media > Photos" section of the sidebar, for example:

It is the only easy way to access your photos directly from another application and will usually suffice for sharing a photo or inserting a small version into a document. But the drawback is, that you have no control over the quality. The Media Browser will give you JPEG version of the current preview, and this will probably not suffice for professional prints. It would probably suffice for a collage of many small prints, but not for a large high-quality print. Rysz already pointed out that professional prints may require a very high quality and the Media Browser cannot ensure this.

Your Photos.library file in Pictures is off limits. It should never be accessed directly by anyone, your images should only be accessed from within the Photos app. You can File > Export from there.

To send out files for printing, if the app doesn’t support accessing your images via Photos Browser, you’ll have to export (or drag them) out of Photos first, say to the Desktop, or a folder.

Read the printing submission requirements carefully. Many such sites/apps have very specific requirements for how to save the images, included their resolution and file formats.