I had this exact same dilemma, and went with the Golf R estate. Picked it up yesterday. I only just managed to keep it under £20k, at a 2017, but I wanted reasonably low miles. If your looking at 2019's for £15-20k they must be higher mile examples. I set my search on Autotrader for under 60k, so I don't know the market on higher mile examples to be fair.
The Seat Cupra is a nice enough car. But sitting in one after having sat in a Golf, you could REALLY feel where the corners were cut. MUCH cheaper feeling interior. The door handles are cheap plastic. I just didn't want to deal with that everytime I got out the car. Although you get a lot of spec for the money, so if you can handle the cheaper feel, you will be rewarded with more tech.
The RS4 Avant is a beast though. That V8 is lovely. But a thirsty thing, and the carbon deposit issue puts me off a bit. Almost like regular servicing having to clean that out, else you do lose a chunk of power. None the less, a beast. But, as with most beasts, they are a bit heavier. And more suited to straight line stuff than the twistier stuff. Plus, unlikely for the fuel economy ever to start with a 3, and way more likely to start with a 1. Not a huge consideration on these cars, sure. But was a touch off putting. I averaged almost 34 mpg on the 470 mile drive home yesterday. And where possible, the cruise was set just under license losing speeds. No way an RS4 would get anywhere near that at these speeds.
335i or 340i Tourings are £10k over budget. Nice and all that, but not in the same league really. Either that or you are going older are leggier than you really want for that money.
I looked at S4 Avants as well. A little more expensive than the Golf R if you want to get one new enough for the virtual cockpit (which I did). But very nice. Although that 2.9T isn't a problem free engine. There is one pretty big flaw, that'll affect them all, and is around a £4k fix. Can't remember off the top of my head what exactly it was. But I remember the price. It's all over youtube to be fair. Nice car, nice interior. Hard to find with adaptive cruise though, another feature I wanted.
In the end, after considering all the fast estates in that budget, to me at least, the Golf R estate was the clear winner for a fun, daily driver dog carrier. To be honest, after considering pretty much all the competition, it wasn't even close. But I was putting fun handling over pure power. Mostly as a result of missing my Clio 197 I guess, and the fun I had in that.