Работа Tor Browser и другого браузера одновременно не влияет на возможности и уровень приватности Tor Browser.
However, be aware that when using Tor and another browser at the same time, your Tor activity could be linked to your non-Tor (real) IP from the other browser, simply by moving your mouse from one browser into the other.
Or you may simply forget and accidentally use that non-private browser to do something that you intended to do in Tor Browser instead.