The 'error', as you put it, is that the password change process (i.e. the changing of the KEK and the re-encryption of the DEK into the EDEK) all happens client-side (except for the part where we verify your old password against the hashed version in the database, for obvious reasons).
'We' have 'access' to your DEK at all times — if you define 'we' as the 'client-facing portion of the app'. All of the encryption/decryption, key management, etc happens on the client-side (i.e. in-browser). Remember, as part of signing in to the app, the EDEK is transmitted from our servers and decrypted client-side so that the client can then use that DEK to decrypt your data.
If we instead redefine 'we' to be the backend servers, database, or even myself personally, then 'we' never have access to your keys nor data.
The fact is, there's nothing special about the password change process itself. It's essentially the same as the sign-up process. Nothing is especially exposed during the password change process that isn't exposed during the sign-up process (again, the DEK is present on the client-side the moment you sign up or sign in, although the KEK is slightly more ephemeral than that).
However, I do understand the implication you're making here, and here's the darker side of it: 'we' (uFincs) could change the client-facing portion of the app to steal your DEK (or your password, or even your data) and send it off elsewhere. This is... just true of any piece of software. It just so happens that, since web apps can be arbitrarily updated, it's a lot easier for us to act maliciously if we so chose (although, at least with web apps, inspecting network requests is quite easy).
So indeed, there is an element of trust here. You trust that I (or the entity known as 'uFincs') won't change the code in such a way that the security of the app is compromised. You also have to trust that we have such security measures in place that make it harder for some third-party malicious actor to forcefully change the operation of the app.
uFincs is not a trust-less system. Unfortunately, due to the nature of web apps (or even most apps for that matter), it simply cannot be. Anytime the code can be updated (and can't be audited), there is effectively zero security (for those who are particularly security-conscious). So if your (the general 'your') financial data is so sensitive that any chance of a leak would be utterly catastrophic, then don't even think of using uFincs.
But I like to think that putting these measures in place (particularly, using client-side encryption, not connecting to banks, not using any in-app analytics beyond our own, etc) is at least a step better — in terms of security and privacy — than what most other services do. And I like to think that, even if it's not perfect, it was still worth doing. Otherwise, I wouldn't have 'wasted' 2+ years of my life building uFincs :)