Rapid tests work very well at not signalling false positives, but false negatives happen all the time. The CDC has recommended "serial" testing in order to better establish someone's COVID status (but people aren't exactly given enough tests or money to do that).

If you ever get a positive "but faint" test, you're positive, a positive result is a positive result. It's an alarmingly common misconception people have that the boldness of the line is some signifier of infection intensity, even though tests can't measure that and don't try to. The CDC should have gotten ahead of the natural inclination people have to downplay results that make their lives miserable but :shrug-outta-hecks:

edit: Some people with long COVID can test positive after they stop being contagious