IMO, pro Slack instances are wonderful for searching & good for many different kinds of media, though not mixed media (i.e. you can upload videos, photos, pdfs (and search over them all, including with speech recognition!) but inserting photos into a message is annoying).
I’m not really familiar with Zulip or Discord.
(Also, I’m not sure with pro Slack instances really qualify for (2) anymore)
I don’t know what “private” means to you, but if you just mean you can control who joins, I think google groups are a good choice for 2 − 4.
Zulip, Discord and Slack are all options as well, though they all (to differing degrees) encourage shorter, chattier posts.
However, these are all very bad for searchability, archiving, multimedia content, and creation of permanent content of any sort.
IMO, pro Slack instances are wonderful for searching & good for many different kinds of media, though not mixed media (i.e. you can upload videos, photos, pdfs (and search over them all, including with speech recognition!) but inserting photos into a message is annoying).
I’m not really familiar with Zulip or Discord.
(Also, I’m not sure with pro Slack instances really qualify for (2) anymore)