I uploaded my resume to a job site. Within a week I was called to meet the HR. They asked me why I was looking for a job and if I was unhappy here. I told them I was happy (obviously, I don't want to lose my job) They told me they won't inform the CEO because it would upset him and it was never brought up again.
I worked for a while and then had to leave. The place was toxic for me.
It really makes sense for small companies to monitor their employees because they can't afford to have people quit willy nilly. So, definitely, I am 100% sure they have monitoring software which detects employee search results.
A sudden TripleByte search result showing up on Google is definitely a red flag that the HR would notice.
Having said this. I would say TripleByte wanting to award badges and making profiles public is definitely a mistake on their part. I doubt they have malicious intent. They just did not think through all the consequences with this move.
Nobody want to lose their job in the middle of the pandemic. Bad move on their part for sure.