How do I get to my photos while using an app?

While in Facebook use the link/button where it asks you to select the photos(s) to upload. Then following the procedure shown in this screenshot:

I put photos for upload in an album that's easy to find in the libraries sidebar.

Which system version is installed on your Mac?

If you already are using macOS 11 Big Sur, you can currently only see JPEGs, when you are trying to use the Media Browser from a different application. If you need to access HEIC files or TIFFs, or similar, export a copy of the photo you want to the Desktop, then open it from there.

For example, I tried to select a photo from my library for uploading with Safari.

Most of the filenames are greyed out and I cannot select these photos. Only JPEGs or externally edited photos are currently selectable.