Currently experiencing the same issue on 1.16.4..
Neither me or the other players with access to the realm can join it, experiencing an ever-lasting "Connecting to Realm" screen, at times replaced with a "Can't connect to realm" after a couple minutes.
I've tried a number of workarounds, such as closing and opening the realm, creating new worlds within the realm, logging in and out of my account.
I'm afraid this issue will not be fixed so soon, as there's little attention to it. Since that's so, I'm planning on cancelling the subscription on this realm, and buying yet another one, while transferring the world in this current one to it. If that also doesn't work, I'll make sure to post it here.
For anyone experiencing this issue, I finally found a fix (sort of).
Try staying away from touching the realm for a day or two, and then try to play in it. After doing that, I was able to play on my realm freely.