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When papers discuss "viral clearance" in regards to COVID, they generally test this by PCR. In other words, your nasopharynx has cleared the virus.
When papers about COVID discuss "viral persistence" they're usually talking about the virus taking up safe harbor somewhere deep in your body. These people are generally not testing positive by PCR.
The fact that I'm seeing a few prominent science people mixing these interchangeably recently tells me just how far we have to go on this subject.
Apropos of the subject, longer term antivirals have been the subject of more than one clinical trial for long COVID and thus far the results are mixed, as would be expected. Here's one for an example:
