What kind of indexing and searching can you do ? I've found Google sometimes struggles with certain things (surprisingly) like searching for a date range if I don't specify the date in the ideal format. For other stuff like "stars over trees" or similar it can work quite well.
I honestly think that the search feature of Immich is better than Google Photos.
Maaaybe AI-based searches like "cat on a red car" are better on Google (but I wouldn't bet my life on it), but Immich applies the exact filters that I want (Google is too fuzzy).
Also, unlike Google, Immich doesn't censor your searches, so I can look up for naked pictures or photos of gorillas, and actually see the results.
Search by date, OCR, AI context, people's face, location, by map, and I probably forget some. And from any result you can then jump to its location in the timeline. Back history navigation works properly to boot. And all of that is very pleasantly fast. I am very sensitive to latency, and Immich is one of the rare software that actually feels fast. Google photo is trash in comparison.