You are cycled for sure, a month in with any doser for bac is cycled, see the time axis on any cycling chart, and those were made before bottle bac came on the scene which speeds it up to about a week or much less (same day as added, fish in cyclers)
only ammonia control matters not the other two common params, none of the testers are very accurate so nitrite and nitrate issues can be found in posts for fully matured reefs as problem readings, it doesn’t make the testers more accurate to assume their every reading is accurate for a cycle tank.
your tester for ammonia is the issue not the bottle bac being dead or weak. A seneye tester would show that you are ready to start. There are no cases where someone a month underwater isn’t able to start, it’s why the cycle charts have the same time frames no matter which book or site they come from
*since our cycle authors, salesman et al have omitted that information from their sales YouTube videos, the end result is now thousands of people buy more bottle bac, to see if they can get api testers to read three params exactly right. The cumulative effect of testing for anything other than ammonia going down in 24 hours is to sell more bottle bac to ease implanted doubt.