Lightroom Mobile and Cloud Storage

To sign out, open the LrMobile settings menu and tap on your name at the top, that will give you the sign out option.

However, can you tell us what subscription plan you are using? If you are using the Photography Plan, which includes Lightroom Classic, Photoshop, Lightroom (includes desktop and mobile version) and 20GB of cloud space, then the issue is that your storage allowance appears to be fully used up, so no more photos can upload to the cloud until you free up some space be deleting some of the images in the cloud. Those users who try to manage a mobile worflow using the 20GB Photography plan will typically wait until the first 20GB of images have downloaded into their Classic catalog, then they will remove all images from the cloud (safest way is to select all the images in the All Synced Photographs special collection in LrClassic, right-click and use "Remove photos from All Synced Photographs". That "unsyncs" the images, which causes them to be deleted from the cloud, which makes way for the next 20Gb of photos to be uploaded from your mobile device(s), and so on. You may have to remove the images from the cloud trash can as well before you can upload more images, though I'm not 100% certain about that. The images are not deleted from the Classic catalog, and many users will then resync them from Classic back up to the cloud....Classic only uploads smart previews, not the full original, and those so not count against the 20GB storage limit.