For some radios, in order to have the headphone jack reproduce the transmitted audio, there’s a built in “monitor” or “side tone” setting that must be turned on (not to be confused with the “moni” function that simply opens up squelch.)
Does the BTech radio allow CAT control? If so, HRD (Ham Radio Deluxe) has a recorder app built in that records both the outgoing and incoming audio. It works well with my Yaesu radio.
The Yaesu FT5DR handheld will record both sides to a microSDR card in the radio. So will their FT3DR and probably their mobile radios such as the FTM500. I wouldn’t be surprised if some of their less expensive models do also.