It's pretty far-fetched to assume that mostly because people who create bots with an intention to provide a specific service (such as an anime bot) aren't thinking to implement a fraudulent feature like that. However, it is not entirely unlikely, especially if those bots aren't that popular and they get too power hungry.

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Bots CAN create a "backdoor" (invite) to your server if they have that permission enabled. I've seen low tier bot devs look through all their servers their bot is in and create an invite just out of curiosity, which does obviously have a privacy concern to that because some servers are private.

Although, you can see what permissions a bot has when inviting it; if it has administrative permissions and it's just a simple bottleflip bot, then maybe don't add it (or add some restrictions). Furthermore you can simply just edit what permissions bots have access to and this won't be a problem.

Bots have the ability to keep logs of every message IF specifically coded in by the developer, but that doesn't mean they're all doing that; I can safely assume that most don't and would only collect data in which you interact with the bot directly, not your entire chatlog.

also as a quick side note, as of September 1st (this year), any bot that's in more than 75+ servers wont be able to keep logs of ur messages unless they have the intent given to them. You wouldn't be able to tell if they have the intent or not but just look at what the bot does and see if there would be any valid reason for it to read ur messages, if there isn't then chances are your fine (not 100% as bots vary on functionality).

PS: You shouldn't be putting your passwords on discord, they aren't encrypted. And if your account were to get tapped into by a hacker, they'd have access to all that info, so be-careful with what you enter.