I am looking for some recommendations on banks that do not require an app, but allow full control online through their website/webapp (without a need to physically go to the bank, apart from things like depositing cheques).
I would like to be able to make use of typical banking functionality, such as owning a physical card, making online payments, etc.
Is there some place where I can find recommendations distinguished by country?
Banking Applications Compatibility with GrapheneOS | PrivSec - A practical approach to Privacy and Security have some recommendations for what works on grapheneos maybe some of them might not require an app if you share your country maybe somebody will know a bank that does not require an app
Unless I’m not understanding the question, there are lots of them: US Bank, Chase, Schwab, Bank of America, local credit unions. I have never owned a smart phone and can access accounts through their websites using a VPN for all of them. They send you a 2FA code via email.
At least here in Germany,
Banking apps are used as a second factor to secure your account. Unless there is another similarly strong, or stronger option available I would honestly recommend against not using the app.
Same strenght includes totp
Stornger includes passkeys
Weaker includes getting a code via email
And absolutely avoid getting a code via SMS. As that makes you vulnerable to sim swap attacks.
For UK, most high street banks will offer a hardware token generator, some (like Nationwide) will send it to you automatically and some (like HSBC) will give it to you on request but normally expect you to use an approved™ smartphone. Santander and Lloyds seem to offer SMS as the second factor for (browser) online banking, so that’s another option.
Oh true some German banks offer them too. Some can even do it with a traditional bank card.
Of course the problem with hardware token generators like Yubikey is that you have to always have it with you, and if you lose it, it’s a hassle.