GDPR doesn’t mention “personally identifiable information” once; it’s concerned with personal data, which is “any information relating to an identified or identifiable natural person (‘data subject’)”.

The rest is correct: the restrictions are aimed at organisations, not individuals.

[1] https://eur-lex.europa.eu/eli/reg/2016/679/oj/eng#art_4.tit_...

The restrictions are not aimed at organisations, but to protect individuals.

https://www.gov.uk/government/publications/domestic-cctv-usi...

"If your CCTV system captures images of people outside the boundary of your private domestic property – for example, from neighbours’ homes or gardens, shared spaces, or from public areas – then the GDPR and the DPA will apply to you. You will need to ensure your use of CCTV complies with these laws. If you do not comply with your data protection obligations you may be subject to appropriate regulatory action by the ICO, as well as potential legal action by affected individuals."

You, as an individual, have data protection obligations, if your ring doorbell captures audio/video about someone outside your property boundaries. The apple translation service seems analogous.

The ICO is pretty zealous though in this regard. To quote recital 18:[1]

This Regulation does not apply to the processing of personal data by a natural person in the course of a purely personal or household activity and thus with no connection to a professional or commercial activity.

[1] https://eur-lex.europa.eu/eli/reg/2016/679/oj/eng#rct_18

It's likely taken the view that "purely personal or household activity" only covers the recording of audio/video in a domestic setting.