I've used the Anker PowerCore mini to top up when out and about on holiday. They hold a decent charge, and not expensive if you google around a little.
For a brand recommendation, I've had two approx 10k Ravpower power banks for years. One since 2015, the other 2018. Both still going strong, and cost under £15 each iirc.
I use a wall charger to charge them. But it's an old low power, one so they charge slow (I understand that slower charging protects the battery life somewhat, but I might be misinformed!)
Amazon unfortunately removed a few of the reliable brands due to review manipulation. Ravpower has worked quite well for me, current 20,000 I have supports both QC 3.0 and USB-PD 15W.
The S7 supports Qualcomm's Quick Charge 2.0 so any battery bank that supports this standard will fast charge the phone. However I would be tempted to go for a USB-PD one instead as that will be more future proof, and should still provide up to around 10W (5v 2a) of power to the phone.
I charge by the wall but that's because both my multi USB wall charger and power bank supports USB-PD to fast charge it. PC USB ports don't usually provide that much power.
Yeah unfortunately Ravpower was one of the brands removed.
I'm not sure on those other brands. A quick look at the reviews seems quite positive but there is one review stating it might not be a true 10,000 battery.
Could check out the Anker PowerCore 10000 PD Redux, it supports USB-PD 18W on the type C port and 12W on the type A port.
Thanks Orcvader. Checked out the Anker Redux, price is very decent at £39.99. But it says supports Galaxy S10 upwards so probably incompatible with mine and it also doesn't look very slim or as slim as other powerbanks I've seen.
That's due to the S10 and upwards supporting the USB-PD standard. Older phones will default to the lower ~10W charging speeds. But as mentioned before USB-PD will be more future proof if you want fast charging.
How slim do you need it? Compared to the other two you linked before, it's shorter than them in terms of length and width, but it is a tad more thicker.
Sadly not QC compatible so it won't fast charge it, but compared to QC 2.0 anyway it won't be that far behind.