TIMATIC, which is what airlines go off on border requirements states :
Emphasis mine
Passengers must have a negative COVID-19 test result. Tests accepted
are: CLEIA/ECLIA quantitative antigen test, LAMP, NEAR, Next
Generation Sequence, PCR, RT-PCR, Smart Amp, TMA or TRC. The test must
be taken at most 72 hours before departure from the first embarkation
point, and the test certificate must be in English. The test
certificate must also specify that the test is based on a
"nasopharyngeal swab", or "saliva", or "nasopharyngeal and
oropharyngeal swab". A "nasal swab" is also accepted if the test type
is LAMP, NEAR, PCR, RT-PCR, Smart Amp, TMA or TRC. Details can be
found at https://www.mhlw.go.jp/stf/covid-19/border_test.html and
https://www.mhlw.go.jp/content/000905811.pdf .
This does not apply to passengers with a COVID-19 vaccination
certificate showing that they were fully vaccinated and received a
booster dose. Vaccines accepted are: AstraZeneca (Vaxzevria), Covaxin,
Covovax, Janssen, Moderna (Spikevax), Nuvaxovid (Novavax) and
Pfizer-BioNTech (Comirnaty). A combination of vaccines is accepted.
The certificate must be in English, Japanese or accompanied by a
certified English or Japanese translation. This exemption also applies
to their accompanying children under 18 years.
This does not apply to passengers younger than 6 or 7 years depending on the school starting age in the country where they reside.
More details can be found at:
https://www.theglobaleconomy.com/rankings/Primary_school_starting_age/
This does not apply to US military personnel, civilian personnel, and their dependents. They must have SOFA status and have the required
documents stipulated in Article IX of the US-Japan Status of Forces
Agreement.
This does not apply to passengers with a consular letter specifying why the test could not be taken.
Passengers could be subject to a COVID-19 test upon arrival and
quarantine for 3 days. Details can be found at
https://www.mhlw.go.jp/stf/covid-19/bordercontrol.html and
https://www.mhlw.go.jp/content/000945853.pdf
Passengers must complete a "Quarantine Questionnaire" through the
MySOS app or at https://arqs-qa.followup.mhlw.go.jp/ . This will
generate a QR code which must be presented upon arrival.
Passengers must install the "MySOS" mobile app before departure or
upon arrival. More details can be found at
https://www.hco.mhlw.go.jp/fasttrack/en/
So, as of 17 September, no airlines will ever let you board without a conforming COVID Test if you aren't vaccinated with 3 doses.
You don't need the test if you are vaccinated