Unsure if Photoshop edits are getting saved back to Lightroom Classic

I have a previously edited image, as a tif file, that I want to fine tune again in Photoshop. I right click, Edit in Photoshop, choose Original and make my minor changes in Photoshop. When I save that file, there is no update in the history saying 'Edited in Adobe Photoshop (date time)'. However, when I send back to Photoshop, the changes I made are still there. Should I see a new 'Edited in Adobe Photoshop' if the image has previously been edited in Photoshop? I would think so since.

When I send a new raw file over from Lightroom to Photoshop, make changes, and save, I do get the History updated.

I am using Macbook Pro, Mac OS 11.3 (Big Sur) and have my apps up to date. For these images tested, the images are on an External Hard Drive. 

Thanks for any help or suggestions you can provide.