Ok as someone that’s used the HTBP a lot over the years.... the point of using it is so that when playing 2-ch sources (CD player, turntable or music streamer) you get the advantage of the sonic benefits of the 2-ch integrated amp. The integrated amp should control the volume for those sources when those sources are in use. The AVR should take over preamp/volume control when you engage the HTBP mode of the IA, thus leaving the IA an a Power Amp, for the benefits of the improved amplifier section of the IA over the AVR. The AVR usually controls all the HDMI switching for more surround sound sources (cable tv, gaming console & blu-ray player).
Otherwise if you’re using the AVR for all sources, then there’s no point having an IA, the preamps being wasted. In this case you’d be better just owning a power amp. No need for HTBP setup.
Dynaudio Contour 20, Focus 210C, DM 2/6, Hsu VTF3 MK5 HP, Oppo BDP-103, Naim Uniti Star, Marantz SR5010, 60" 4K Samsung LED LCD, XBOX ONE S