Can I access programmatically (AppleScript or?) the Get Info lookup option of a photo in Photos?

On Mac open the Script Editor. Under the File menu select Open Dictionary. Run down the list until you find Photos and open it. In the top LH pane select Photos Suite. This gives you the full list of things that Applescript has access to.

I don't use photos so I don't know what you're looking for, but the Media Item contains the following. If that's not what you want then have a look at the other stuff. Scripts can only use or see the things which are in the dictionary.

You should be able to do what you want with Keyboard Maestro. It can mimic your moves like in this example of turning off and on a CSS file for Safari:

You could program it to open the Info window for a selected photo, select and copy the text in the into pane and paste it into the Caption field. All with a 2, 3 or 4 key keyboard stroke like Shift+Control+Option+i.

Dan Hinckley wrote: … a bird photo will search for the bird ID using the Get Info. Can I extract the lookup results

You can just select the text and copy it:

Here I've selected the text for the Red-Shouldered Hawk. It can be copied and pasted into the Caption filed, for instance.

Use a Smart Album with the criteria: File Name contains "xxxx"

or if the name is in the Title field: Title contains "xxxx".

It's much more efficient (i.e. better) than searching in the text field at the top of the library window.

I'm not much into scripts or shortcuts, but the bottleneck seems to me to be the part where you have to click on that little circle over the object--I haven't seen a command for that. Sometimes there's more than one bird, so a command would have to account for that. Someone here might know for sure. Maybe the best thing in the mean time is to let Apple know you'd like that feature:

Feedback - Photos - Apple