This might seem like a nitpicky point, but the way you’ve worded it sounds like you are talking about a fetus that has existed for six weeks (“They just incorrectly think a fetus is a person after six weeks”). In fact, the Florida law bans abortion at 6 weeks gestation, not at 6 weeks from conception.
The law in Florida clearly defines gestation as starting on the first day of the woman’s last menstrual period.
On average, a woman with a 28-day cycle will ovulation on day 14 of her cycle. (14 days after the start her of her period.) The egg is then fertilized within 24 hours of ovulation. So at 6 weeks gestation, the fetus will have existed for 4 weeks. In that case, the woman could only have possibly known she was pregnant for about 2 weeks at the time the ban comes into effect.
For women with longer cycles, the those numbers be even more restrictive. If you have a 35 day cycle (which is still a normal cycle length), that would mean on average you ovulate at 3 weeks. So at 6 weeks pregnant, the fetus will be 3 weeks old, and you will have had 1 week during which you could have possibly known about the pregnancy.
For a woman with a very long or irregular cycle, it’s possible that 6 weeks would be before she has ovulated, so before the fetus even exists. This type of thing is more common in teenagers or perimenopausal women, but it also happens to many women who have hormonal issues such as PCOS.
Since the law clearly defines gestation age by the first date of the last menstrual period, as opposed to defining it by something actually related to the fetal age, there isn’t any room for doctors to be reasonable and use dates that actually correspond to the fetal age. This means that the law essentially bans all abortions for many women.
I don’t think that this is just some unintentional oversight. I don’t think that laws like this are indicative of people just being confused about consciousness or whether a “heartbeat” makes a fetus a person. If they cared about heartbeats, they could define the law based on heartbeat. But they don’t. Instead they use a definition that blocks more abortions.