Many business premises in the UK, such as coffee shops and restaurants have been requiring the customers to sign in using the NHS app and a QR code. The other method I have seen is a paper list.
I suspect the QR code is not the problem, but software controlled by companies answerable to the emperor would be.

Concerns over Chinese apps and tech is an interesting problem:
1 Chinese companies are required to co-operate with the Chinese intelligence services by Chinese law. I'm not aware of such laws in the west & co-operation may or may not happen. There have been many reports of What's App refusing to allow back doors to get past their encryption.
2 Some of the US objections to the likes of Tik Tok and Grindr under Chinese ownership may be political. As China has restricted operations for the likes of google and so on for many years, some reciprocation is reasonable.