It's customary to distinguish two aspects of a COVID test's performance:
(For further explanation of these concepts, see: https://questdirect.questdiagnostics.com/myquest-faq1/QuestDirect/COVID_1077.htm )
The relative importance of sensitivity and specificity varies depending on the application and the audience for the test:
From a public health or practitioner standpoint, it's desirable to have a test that is both highly sensitive and highly specific. Low sensitivity ('frequent false negatives') means one misses many cases where the virus is present, leading to increased transmission risk; low specificity ('many false positives') means one incorrectly identifies individuals as positive, leading to unnecessary burden on the healthcare system, unnecessary absences from school or work, etc.
From a individual risk standpoint, a test which is highly specific test may still be very useful, even if it isn't very sensitive. I.e.: if a negative test is very likely to indicate a true 'negative', one can simply postpone a social engagement on this basis, and test again when convenient.
The most accurate overall testing technology currently is 'molecular'. 'PCR' is a type of molecular test, as is 'LAMP'. (For more details on this, see https://www.technologyreview.com/2021/05/04/1024450/at-home-covid-test-review-accuracy-binaxnow-lucira-ellume/.
LAMP tests can be performed at home, and seem to be as specific as PCR. See: https://www.southampton.ac.uk/news/2022/01/lamp-testing-accuracy.page
Also see: https://www.theverge.com/2022/6/3/23141813/molecular-covid-19-test-otc-pcr-fda -- which references Lucira as an 'OTC' test (which simply means 'over the counter').
Also: some info from Lucira on the Positive Percent Agreement (PPA): https://www.fda.gov/media/143809/download