I do not run Immich but their privacy policy states:
Locally Stored Data: Immich stores all your photos, albums, settings, and other metadata locally on your device. We do not have access to this data, nor do we transmit or store it on any of our servers.
https://immich.app/privacy-policy
Additionally in their docs I can find no mention of connecting to outside services. I do see references to downloading hugging face models.
https://docs.immich.app/features/facial-recognition#how-face-detection-works
LewdLemon@sh.itjust.works 6 hours ago
Immich is entirely free and open-source software and got a grant from the FUTO Foundation, which is fiercely pro privacy. As such, it does not engage in any data sharing. Development is financed through the grant and purchases of the server licence (I got one; it’s ridiculously good software).