digged several google results, the blog and this column refer some thing may helpful.
page=1
parameter works only for multi-page video collection e.g. this Satfiled OST Collection: set page=5
at https://www.bilibili.com/blackboard/html5mobileplayer.html?bvid=BV1sP411Y7am&page=5&high_quality=1 that player will stream the 5th video of collection. I guess you are right -- it's not an efficient parameter for single page bilibili video.
as for aid
and cid
: aid
stand for av code which was changed to bvid
years ago, these articles see it as a legacy for compatibility. And I assumed cid
stand for clip id, because bvid
identified the whole collection while cid
become the identification of single video in the video collection, that might be useful for web video scraper rather than embed video.