I would just like to mention that I had changed my Login and Security for today (at around noon) from e-mails to an authenticator app, but I noticed that it asked for a code EVERY time I was logging in to GOG! Surely it's faster to give an authenticator code from your cellphone, than having to open your e-mail, but at least with the latter method you aren't asked for a code EVERY time you log in to GOG!! So, I changed the method back to e-mails.

Why are you logging out? We're long past the day of unattended terminals with no password locks.

I don't use a code to open my PC at home. But sometimes I log in to GOG from work's PC too (in which I use a code to open it), so I have to be logging out (from GOG I mean).

Edit: the work's PC can be "entered" at any time by the people (co-workers) who monitor the overall network.

They need to implement a YubiKey option.

This behavior (which GOG should provide an option for, which would only trigger once the 'differing device or location' condition has been met) can be a bit annoying (especially if one is exclusively reliant upon their phone for generating TOTP codes), but, there may be some alternative methods which may make this process more streamlined for you. Though, this depends on your operating system preference (and/or availability in circumstances outside of your control, such as your workplace), as well as your level of technical proficiency.

As an example: for GOG (and other sites which fortunately support Time-based One-Time Password/TOTP), through the usage of shell scripting (and a small number of programs), each time that I select a given web site-specific sign-in/log-in menu item, as a six-digit code prompt is detected, the relevant Base32-encoded string is decoded, while the resulting output is fed to totp. This immediately yields a code (based on the current time) which is then automatically inserted into the appropriate text field of said web site. This very same process functions well on local (such as my desktop and single-board computers, as well as my Android phone) and remote (somewhat trustworthy computers which I occasionally have physical access to) Linux-based (or OpenBSD-based) devices running the X Window System.

Anyways, my point is that whether it is the aforementioned insanity, or a simplified (as in: requiring the least amount of user interaction) authentication application on your mobile phone, the perceived pain can be alleviated.