I'm so thankful for the BBC.
I listen to Radio 4 through the day when I'm working on things that don't need my full concentration.
It's the alarm that wakes me at 0630 and I often listen to the news before bed.
Adverts drive me insane. It's a national treasure and I'd pay the licence fee again just for R4 + Sounds.
Also listened in the car but since they've recently shut down the LW tower I can't receive it anymore in the midlands, only occasionally get FM signal.
It might not work in your scenario, but I too listen to radio a lot and found the signal issues annoying. My car is pretty old and doesn't have aux/bluetooth input so I can't plug in my phone and use the Sounds app, but I got a bluetooth to FM signal transmitter and now listen to my phone through my car radio, including a lot of streaming radio.
FM dongles for smartphones and tablets are a thing. You can stream your own playlist or podcasts over your tuner (and anyone else's within a small radius). The devices are cheap but effective.
I could pick the LW up at night in my car from Slovenia!
I listen to podcasts all day while working and I am JEALOUS of your access to radio 4 and sounds. There is so much just insanely killer content coming out of the BBC in those avenues.
Lots of Radio 4 programmes are available as podcasts, and it is possible to stream BBC radio outside the UK without a VPN - see the links here:
http://www.radiofeeds.co.uk/
bbc.co.uk still allows listening to all stations live and yt-dlp has no problem to download shows, you just got to find your way to the correct page that doesn't trigger a redict to bbc.com e.g. https://www.bbc.co.uk/programmes/m001qng7/episodes/player