That… seems reasonable? My bank does that with their website and their mobile app. I was able to setup 2fa using a totp app, so i don’t rely on sms for that part
To hack the banks app you have to find an exploit in iOS or Android which would allow you to read the other apps private storage, which is borderline impossible now. To hack the banks website you just have to buy some random browser extension and add malware to it, or break into someones NPM account and distribute it there, or any number of ways to run code on someone else's computer. Something very achievable by an individual.
Does it? The browser doesn't do anything, the person sitting at the computer where the browser is running is what performs the actions. The reauthentication and 2fa is meant to authenticate and authorize the user, not the browser.
The attack vector of someone else using your phone using an app that doesn't require (re)authentication is independent of the browser or the app itself being trusted. That your bank doesn't periodically require some kind of re-authentication for their app is a security hole, but because the device could fall into the wrong hands, not because the code/app/browser used to access it isn't trusted.
If I steal your device, and you didn’t have faceid, I have both factors. But if I steal your password, or find it in a leak of another site because like most people you re-use passwords, then I only have one factor. It still provides a fair bit of security because of that.
2FA on the same device secures against your login credentials becoming known to another party, e.g. by fishing, password reuse, database leaks, etc., which are real threats. It is not meant to protect against someone being in possession or full control of your unlocked device, which is of course also a real threat, though possibly less common.