My issue isn't that those apps aren't available for Linux. Even if they were available for Linux I wouldn't install a bank app with those permissions. I wouldn't install that on my primary Android phone (I guess there's a good likelyhood I couldn't, since I run rooted Android).
I'm not sure what I would do in that position. Maybe get a separate phone just for banking? I don't know, it's really tough. I sympathize.
But yeah, the Pinephone is not going to solve that problem, banks would need to move over to open standards for authentication through apps that are trustworthy. Just releasing their apps for a smartphone wouldn't be enough. At least any "security software" that can run on desktop Linux can also be run on your phone, assuming it doesn't freak out over the hardware, and assuming you're willing to tolerate it.
Sure, if you want an app for an open source platform like Linux, that may take a lot longer. I think there is already a common platform for this, but not many banks offer it.
The government isn't forcing anyone to install the ICP-Brasil root certificates; if you don't, the government websites will just show as untrusted in the browser (since they're signed by one of the CAs which chain to the ICP-Brasil root), but other than that they should work the same. Things might be different if you are authenticating your identity to the government with a certificate stored on a smartcard or USB key, since these certificates are also signed by a CA which chains to the ICP-Brasil root; I don't know if adding the ICP-Brasil root to the browser is necessary to make that work.
As for the banks, AFAIK the government doesn't mandate how they approach their online banking security; their use of that invasive "security software" is probably mostly path dependence at this point. It was very common to see computers infected with malware designed to steal online banking credentials from the browser, and that "security software" was supposed to block that kind of malware (for instance, by blocking the browser accessibility APIs whenever the user goes to an online banking site). Things are already better than in the past (that "security software" used to be Windows-only, for instance, so Linux users couldn't use online banking).
And yeah, all the bank apps I have on my phone require contact/location/camera permissions (the camera permission is unavoidable since they have to be able to read the QR code for PIX payments, and boleto bancário barcodes), and for at least one of these apps, I strongly suspect it's using the location permission for security purposes (the location indicator always lights up whenever I log into that app). It wouldn't surprise me at all if it also rejected rooted devices.