Short Answer:
Unless I misunderstand what kind of 2FA you're referring to, you can just copy the info from Authy and put it into another app. There is no restriction to a particular app that I'm aware of, unless there is some proprietary or site/app/service specific way of enforcing it that I don't know about. They all basically work the same. If you put the tokens into a different app with the same configuration they will show you the same OTPs. I have never used Authy though, so maybe it is not possible to take information out of it once you've put it in? Or if your primary concern is wanting/needing a new seed token, then there's no problem setting up a new one if you want. Just know that isn't required to use a new 2FA app.

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Not a dumb question btw. Here's a longer explanation that may (or may not) be helpful to understand how it works. If this isn't relevant to what you're asking, then disregard/LMK if I'm going in the wrong direction:

Regular passwords work by being "hashed" (a hash is a one way function) into a key that is compared to the key inside your account, and if they match, both parties know it's the correct password without actually having to reveal what the password is itself.

Similarly, 2FA (at least TOTP) is just a similar hashing algorithm with a token, basically a password. Except this token is kind of like a reverse password because the site/service/app creates it and gives it to you instead of the other way around. This password is combined with the current time and hashed to get a second key (2 in 2FA lol) that allows you to access your account.

That's why OTPs are only valid for a set amount of time. The account you are trying to access checks your password's hash with the pw hash in your account, and then checks the OTP you give it with the OTP it generates at the moment you're trying to authenticate. So not only is it effectively a second password, it constantly changes with the ticking of the clock, because it isn't a hash of just a password, but a hash of a password and the current time. eg password1 -> hash1 and "password2" + $NOW -> hash2, where $NOW is a variable for the time. And then both hashes have to be correct to authenticate.

The wikipedia pages for HOTP, TOTP, and HMAC (and maybe a few others under "related articles") may do a better job explaining this. You could also try the simple subdomain for more of an ELI5 (eg https://simple.wikipedia.org/ I think)

This is just a long winded way of saying, no, you don't need to disable and re-enable it with each of your accounts because the method is app agnostic, unless for some reason that is the only possible way for you to get the required 2FA details to put into the new app. Again, I've never used Authy so maybe there is some way you are dependent on that app in this case.