OJAD's Suzuki-kun/Prosody is simply wrong. It often is.
The correct accent is (aka {LHHLLLHL}, though the will be lower than the due to terracing, which is not possible to represent with this site's LH notation)
Namely:
* is [3] and stays [3] regardless of whether it's followed by or not (unlike for example, which will turn from [2] into [0] when followed by ).
* is [0] standalone, but when modified by a proceeding phrase, it becomes [2] (odaka).