How can I use my save files for TBOI after switching to other Steam account?

[amarantha]

It's the same PC, so all save files must be the same, but the game doesn't recognize it and treats it as a complete undone game.
What can I do for my new account to "see" those files?

[Bogopo]

Each account has its own save file

Did you try overwriting what's in the "My Games" folder? This is just a backup. The actually used game save files are located at;

Program Files\Steam\userdata[steam account ID]\250900\remote

on Windows, and at one of:

/home/[username]/.steam/userdata/[steam account ID]/250900/remote
/installpath/steam/userdata/[steam account ID]/250900/remote 

where: /installpath ~ /usr/games/steam (depends on distribution, check e.g. dpkg -L steam)

on Linux.

250900 here is the sequential gameID in Steam's database.

There are various ways of finding out which accountID is which account. The simplest is logging in via a browser and looking at the GET request for the profile page. The URL should contain the accountID, also known as 'steamID' (it's an alphanumeric sequence of around 16 digits).

Since you have two steam accounts, each Steam account will have its own folder.

They are stored there and only backed up to the "My Games" location. Make a separate backup of these files, then try copying your old files over them.

Sources: https://steamcommunity.com/app/250900/discussions/0/1639790664938175128/ , https://www.maketecheasier.com/find-steam-id/