"spying on a Government", I'm not aware. Government are generally more careful than the general public in selecting their suppliers.
OTOH several incidents exists where Chinese phone vendors have been accused of sending data back to China, in not exactly kosher fashion.
- The rather obscure "Star" company was mentioned in a comment (by Brian Z). This is from 2014:
A research firm says that a popular bargain-brand Chinese Android smartphone comes with a hidden extra feature: permanently installed malware that sends users’ personal info to a secret server in China.
The Star N9500, not common in the U.S. but widely available in Europe, is widely regarded as a cheaper variant Samsung’s Galaxy S4. It’s got a similar look and features, but it’s often sold for under $160, a fraction of the S4’s cost.
But you get what you pay for, apparently. German security firm G Data says it’s found that the phone comes bundled with extensive malware—embedded in the N9500’s firmware, so it’s impossible to uninstall—which allows the phone to track all of its user’s personal data. The malware also blocks security updates.
- And that was hardly the only such incident. 2016:
Security contractors said they’ve discovered pre-installed software on some Android phones in the U.S. that sends a variety of users’ data to China through a secret backdoor.
The software tracks users’ whereabouts, whom they talk to and the content of their text messages, sending the information to a server in China every three days, The New York Times reported. It isn’t clear whether the secret backdoor is being exploited for advertising purposes or by the Chinese government for surveillance. [...]
Blu Products, a Florida-based handset vendor, said 120,000 of its phones had been affected. The company said software on its phones had been updated to address the backdoor.
Blu is a relatively minor player in the North American smartphone market, but it has attracted significant attention in recent months. Its R1 HD phone became Amazon’s top-selling smartphone for a time in August after the online retailer began offering the phone for $50 to subscribers of its Prime service willing to accept ads and pre-installed Amazon apps.
Nokia phone brand owner HMD Global is understandably nervous about Finland investigating claims that its handsets send sensitive data to China, and it's trying to clear its name. The company said in a statement that it "mistakenly included" the device activation software for Chinese phones in a "single batch" of Nokia 7 Plus phones meant for other countries. However, that data was "never processed" and wasn't personally identifiable, according to the company. It was fixed through a software update in February 2019, and "nearly all" phones already have that patch.
- Slightly aside, a report from 2023 says that multiple Chinese vendors do not disable their tracking systems for the Chinese market when the phone [with such firmware intended for the Chinese market] is used abroad. (That's hint for anyone buying Chinese phones in their Chinese-market version e.g. directly from Alibaba etc.)
So, of course [Western] government entities are worried about such occurrences.