Sony HT-Z9F - switching to HDMI 1 brings up soundbar screen and not TV
Setup for now is a bit older TV (Sony 65 950G is on the way!) - with the Z9F plugged into the ARC HDMI 1, PS4 into HDMI 2, Roku into HDMI 3. The cable box is plugged into HDMI 1 on the soundbar.
Problem: when I switch inputs on the TV to HDMI 2, I get the PS4 screen. When I switch to HDMI 3 I get the Roku screen. But when I switch back to the Z9F, I get the Z9F selection screen instead of the cable TV, where I have to select HDMI 1 on the soundbar screen to get TV back.
I can't see an obvious way to get it to just switch directly to the cable box/TV. Anything I'm missing? (I'm sure there is, but what is it?