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After driving the car for a few months I still don’t like the way the radio UI works. Muting the radio with the volume switch turns off the display and goes back to the screen to pick an audio source. I would much rather it stayed on the last source and just muted the volume. That way I can see what’s playing on the radio or just pick another station to start listening. Most cars don’t assume you want to switch sources when muting.
I too have been frustrated with the lack of a physical Pause button. The **** under the main screen is an On/Off button, as you probably know. Your comment encouraged me to find a better solution in the manual, and there is a designated Mute/Pause function hidden within the audio source/Mode selector, shown in the screenshot below from the Multimedia Owner's Manual. Since you have the 450h+, you should have the dynamic touch buttons under Type B, as I do. I haven't tried it myself yet, but hopefully this function addresses your screen display issue.
Update: I’m able to isolate the issue OP is describing only to using the regular Radio. In that case the Mute function above resolves the screen-changing issue that occurs with On/Off.
When I use Apple CarPlay, the On/Off and Pause function seem to have identical results with no screen change, so no issue there.
I find the Mute/Pause function in the Mode button to be too slow, since you have to hold the Mode button a while, and if you release too quickly it changes the audio source. In the case of Satellite Radio, it’s quicker just to touch the Pause button on the Radio screen if you want to keep the music info showing, or use the physical On/Off **** when on a different screen to start with. However for FM Radio, it looks like there’s no button on-screen, so holding the Mode button would be the way to go. It would be a good suggestion to Lexus to add a Mute button on-screen for FM like with XM.