Depends on the child.
As for "why would he be anxious about Covid?" that's because, even if the parents have been relaxed and pragmatic, most children have still been exposed to very scary messages for almost a year now. They overhear news on the radio, they see signs on bus stops ("IF YOU GO OUT YOU WILL KILL PEOPLE"), they hear things in the playground, they are constantly reminded of socially distancing, handwashing, etc.
In fact the only way to get small kids to comply with (necessary) precautions is by constantly reminding them. Even if you do this very gently, they still absorb the message of "these rules and big changes are very important because of the virus". So is it any wonder that kids pick up on the fact that the covid is scary and dangerous?
Yes, they are unlikely to get very ill but it's hard to get that nuance across. Even when you do convince them kids are fine, they still worry about their parents!
Some children will take it all in their stride, others will feel very anxious. Not because they are wet or wimpy or because their parents are turning them into "snowflakes".
But because kids are different.
I wouldn't outright lie, but if the kid is going to be scared then I might try to avoid telling them immediately. Then mention when the isolation is nearly over that it was covid, but everyone in the family is fine etc.
I have been really emphasising to my dc that Covid "doesn't make kids very sick" for ages, but even so they were quite worried when they heard that some of their classmates had it (who were all fine, thank God).