This "at work" qualifier I don't think is a meaningful distinction when considering if something is cancel culture.
You're saying that employers can fire employees for speech made during employment. You're correct, in many cases can. But whether something is cancel culture I think needs to account for the impartiality and fairness of a response, which is always difficult to define. For example, if the team that Kaepernick was employed by had a policy that was against all forms of political and social speech while at games, and this was fairly enforced for all players regardless of their speech, then it is not cancel culture. If they made a judgement call that Kaepernick's political/social speech was specifically unpopular and for that reason terminated his employement and blacklist him (as some say effectively happened) then that would seem to be cancel culture, regardless of whether the entities involved had the right to do so. Also you say that you doubt Kaepernick would have been penalized if his speech had been totally off the field - I tend to doubt this because as a NFL player he has some celebrity status and his team would likely consider him a representative of the team both on and off the field. Even a minimum wage job I had long ago during training they told us that they always considered us to be representing the company on and off the clock. Of course he kneeled on the field "at work" as you said, so we will not know for sure how his team and the NFL would have reacted if he did not kneel on the field. Suppose a person of political Party A talked politely about their political views in the breakroom, while everybody else at a company talked politely about their Party B political views. And the Party A person got fired for talking about politics at work, but all of the Part B people kept their job. That would be cancel culture, no matter the value of "A" and "B".
Take social media de-platforming. Just like an "at work" distinction (employers have broad latitude to make employment decisions) social media networks essentially have an "on their network" power to ban people violating policies. It could be cancel culture if they were specifically banning people because of their political views. But if their policies concern things like e.g. encouraging hate, violence, medically unsafe behavior etc. and are written and enforced impartially then enforcng these policies fairly is not cancel culture. But if they specifically ban people who e.g. are fiscally conservative then that is cancel culture.
Basically I'm saying that in my opinion for something to be cancel culture it has to be based around trying to go after people for their specific views in a biased fashion. And it is cancel culture no matter whether it is done by pundits on commentary TV shows, private individuals on Twitter, by employers to their employees, by social networks, by Presidents of the US, etc.
But it is does seem to me like it is fair game (not cancel culture) to go after people who espouse hate (too much of that on all sides in politics today), who support violent acts, who oppose a fair democracy, who appear to have committed crimes, etc. There is a similar phenomenon to cancel culture which is outrage culture - amplified by social networks people can get very outraged about something before a lot of information is out there, and before an accused party can even give their side of the story. I think this is a kind of separate issue, even if it has some commonality with cancel culture.