I get paid biweekly, which means the same as semiweekly here

Interesting, I've come to understand those prefixes to have the opposite meaning. I looked into it, and apparently the actual usage of bi vs semi is not super consistent, and has been historically ambiguous and especially difficult because of how confidently people tend to believe others share their understanding on the words.

Take the term biannual, for instance:

https://www.merriam-webster.com/dictionary/biannual

You'll notice a lot of the words you listed include both "twice per" and "once every other" in their dictionary definitions. Of course, dictionaries are descriptive and not prescriptive indicators of language, and I think it's fine to argue one's case to keep the terminology consistent at least within the bounds of a conversation.

I guess the takeaway is that it's good to have a context under which the terms are consistent, like with banking, but also important to understand that there are other contexts with definitions that differ, and that those different contexts aren't incorrect.

Nobody tell banks about fortnights

Both work with the following caveat:

the "twice" is "once with similar gender, once with different gender"

the "every other" is "every member of similar gender and then again with other gender"