For the creation of animated Photoshop GIFs, go to the window menu and timeline and then click the frame timeline in the center of the timeline panel (you may have video timeline available but with the M1 mac this is not currently available)
As with anything to do with the application, there are 100s of possible ways to do this. I am going to animate a shape layer. Start with an empty document, background is not going to be used. Create the shape layer via the ellipse tool or custom shape tool etc and use as shape layer and set the fill for the design to be animated. You should now have one single layer and the background ()whichy can be removed by deleting it)
Go to the layer menu and duplicate layer (hold down the alt / option key if you don't want the dialog to appear). Repeat this multiple times to create a lot of copies of the shape. Now you can see multiple copies of the same shape
Select all the layers in the panel and then go to the opacity setting and set to 20% etc so you can see through all the layers (set it back later) - it makes it easier to see the animated layers, difficult if they are blocked or hidden. To make it easier to work, start from the bottom layer to the top, so deselect all the layers above the bottom two. Leave the bottom shape in place and select the above shape layer and move it or re-size it or change the gradient etc.
Go to the next layer above and set that to visible again and add your shift or rotation or scale etc and then repeat this for all the layers above in turn.
Return the opacity for all the layers back to 100% again
Select all the layers in the layers panel and set the opacity back to 100%. Go to the timeline panel and right side menu and make frames from layers. If you have an extra, you can always select such as the background and then use the delete command and the image will be removed and will not appear in the final result.
Select all or set the time an image at a time, and go to the time entry and set it to 1.0 second etc. You can check out your video by clicking the play button on the timeline along the bottom
Go to the file menu and export and save for web and set the export to GIF and go to the bottom and set the looping (forever etc) and click save