The team I was on at work number of years ago had to hash this exact thing out because we had a "biweekly" status and was confusing people. We ultimately landed on not using the term.
There are not two definitions. The prefix (bi) modifies the root (week). The suffix (ly) modifies the combination (biweek). Biweekly will always mean "once every two weeks" due to the order in which English dictates that the modifiers operate.
So, the usage of biweekly as a synonym for semi-weekly is sufficiently high enough to land it in the dictionary, alongside a definition of every-two-weeks, and make biweekly an ambiguous and confusing term.