I disagree, I believe TOTP belongs firmly in the "something you have" category. You cannot memorize TOTP password, nor you can store in your password manager. You also cannot pass that knowledge to another person. So this is more like a public key than a password.
Ultimately, everything is "permanent, unchangeable secret", including private key and biometric data. Where the data is stored and how is it accessed makes all the difference.
I could not find the original definition of "something you have", but modern standards like PCI actually give OTP auth as an example of "something you have" (p. 4 of [1])
(I am not looking at the degenerate case of running TOTP app on the same device / same security domain -- it does not describe most cases, and there are some fairly straightforward technical measures to defeat this)
[1] https://www.pcisecuritystandards.org/pdfs/Multi-Factor-Authe...