In my notifications, it states "Your 0m 41s 667 run in Hypixel Bedwars - 3v3v3v3 Win - Win With Party has been verified - 23 hours ago," However, the leader board still has not updated. Despite what the notification says, the run has not been verified in my profile nor on the leader boards. I just want to make sure that the run is still in the verification process and has not been accidentally kicked out due to some error.

Thank you, Tempestu

Probably this:

https://www.speedrun.com/the_site/thread/itfu4

It doesn't look like the run is on that leaderboard at all. Do you see it in your pending runs page? (The hourglass icon)

Yeah, it's still pending. But I want to make sure there were no errors since they, for some reason, gave me a verified message.

Well, no idea what happened there, but it looks like the run got verified and then immediately sent back to re-verification queue by the mod team. There is no error here, but you can ask the game moderators about that if you want.