So I bought my BMW based off my car share trips to work. When we first started sharing lifts, my buddy had a 2015 BMW M235i. (2 door) - At the time I still had my 3.2 Elite. His 3.0 petrol was hugely more powerful, frugal and sounded just as great if not better thanks to the exhaust. (stock BMW)
Chalk and cheese type of cars and the age at which they were designed/built. But he would easily crack 30mpg and he drives like TB...
So when I started looking for a replacement thanks to ULEZ, I was drawn to an N55 block 3.0 petrol BMW. From what I see generally very reliable unless you go track with them and tune them up hard.
Pop these engines in Eco mode and it allows the car/engine to coast. This I found has a big effect on fuel use and can really make it drop. It's also very efficient on the motorway, even for a short period. I often join the M25 after leaving work with MPG around ~24-27mpg. Usually like to win the traffic light grand prix drags now

But just 15 mins and it's low 30's and I'll average 33mpg or so by the time I'm home. That's sitting in the BMW lane as well, not doing 60. These engines much prefer doing 75-95mph.
I could never find a m235i in the spec I wanted, BMW's are a nightmare due to options when looking second hand. So you have to go through all the photos in detail to see what it actually has. I wanted Pro Nav, Parking Senors (front/rear) *yes each was an option

, memory mirrors and cruise. But even this basic shopping list was hard to find, always one would be missing.
Stroke of luck and I found my 435i with all the trimming on it plus ones I did not expect. (HUD, Memory Seats, Adaptive Lights)
Not sure this engine and more weight would help in the 5 series, I do notice the performance loss between m235i and my 435i, but his was 325bhp mine is 302bhp. Think the B58's would be a better choice and a stage one remap brings those up I think to nearly 430bhp.
At some point I'm very tempted to Stage1 mine, as it would go from 302bhp to 380bhp!! But I also need some pocket money to upgrade the charge pipe first.
If little fatty can get over the badge, I think this engine (or B58) in something like a 4 series could suit him. I don't find the ride harsh, as this was before the "M" lite type was officially born.
Current car my lift share buddy has is a 2021 m235i, but this is the 4 door one and "only" a 4 pot petrol but still makes 300bhp. We find mine sounds a heck of a lot better and not a massive difference in fuel use.
To sum up, 30mpg on a mixed drive into outskirts of London is no problem. Longer runs, mid 30's very easily even if cruising in outside lane.