81961 a legit apple text message?

When I receive authentication codes it is to my trusted devices, not via a text so I'm not certain of the exact wording if they request a text to be send to a trusted phone number. After they enter your Apple ID and password, all of your trusted devices automatically receive a notification before a code can be sent via text message to a trusted number. I don't know of a way to have a code sent by text without first notifying all trusted devices or without having a trusted device in their possession.

See the following from Two-factor authentication for Apple ID - Apple Support

If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text message or an automated phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device. Learn how to get a verification code.

There may be a method but I don't know of one. To be safe, you may want to change your Apple ID password (they need to enter your password before the code is sent). See: Change your Apple ID password - Apple Support

I got the same text this morning while I was sleeping, PLUS an email sent to my email address saying that someone tried to reset my password and get a passcode. I most certainly did not do this while being asleep. Everything on Apple's community discussions is saying that this is a scam and don't click on anything within the text and don't use that code for anything. I changed my password and made it sign out of all of my devices. I also checked the Find My app and saw a laptop on there that I did not recognize, but it could not find a location on it so I have it set to erase everything on that laptop the second it is turned on, just in case that's a scammer (there is a possibility it could be my old laptop floating around my house somewhere, but I highly doubt it.)

I just got the same text message which got me worried BUT it also said "Don't share it with anyone" which doesn't sound very professional/legitimate.

It is a scam. Among other things, Apple two-factor codes are 6 digits, not 5.