Commuting and recreation scooter with handlebar brake lever

It would help if your post were more specific about what you mean by "scooter". At first, I thought you were asking about a motor scooter, but on closer inspection, I think you are asking about the type of scooter built with a long, low platform one stands on with small wheels at the front and back, and a tall steering tube at the front. E.g. something like this:

In either case, I'm not entirely sure that questions about that type of vehicle are on-topic here. But in the spirit of helping and giving the benefit of the doubt…

Knowing exactly what options you are considering would help a lot, as even between different examples of the designs you mention, there may be important differences. That said…

Does this type of brake perform adequately for an adult (70kg) travelling around town?

Any scooter should include documentation of whatever its designed maximum weight for a rider is. As long as you are within the stated weight limit, the scooter should perform adequately, with respect to supporting the weight, maintaining safe stability for riding, and braking performance. If it did not, I would expect the consumer-protection agency in your jurisdiction to have something to say about the matter.

Would the additional handlebar-mounted lever be useful or prove ineffective for rapid braking?

Frankly, I am skeptical that any brake at all is really that useful for a rapid stop. I can see using a brake to modulate speed, especially if coasting down a hill, and for gentle stops. But one should not be traveling very fast on a scooter like this, and in an emergency where an immediate stop is imperative, I would expect it to be much more reliable to just hop off the scooter and come to a running stop on foot.

There simply isn't much wheel contact area on the road to effect strong stopping action. As compared to a bike, there's some improvement in the friction-on-tire design because you're naturally shifting your weight back onto the wheel providing braking power, but it's probably still going to involve a significant amount of skidding (which not only wears out the tire much more quickly, but greatly reduces the friction that is slowing you down).

At a safe speed (e.g. in the ballpark of 10 mph/15 kph), it should be safe enough to stop yourself on foot. If you're traveling twice that speed, well…trying to hop off is likely to be very dangerous, but it's not like you're going to get good braking performance staying on the scooter either. That's just too fast for that kind of vehicle.

Is a rear disc brake a desirable option for occasional use in fair weather?

"Desirable" how? On the plus side, it might reduce wear and tear on the tire and friction surface applied to the tire. So there's that. On the other hand, it adds another system to the scooter that now needs maintenance. Either way, I don't think you're going that a disc-brake system is going to improve braking performance, and it might even be less effective, since you're less likely to be shifting your weight back as you apply the brake if using a hand-operated brake.

Personally, if it were me considering this purchase, I would focus on deciding what it is I really want. At that price point, I don't think you're going to find something suitable for anything other than the shortest commutes. It's really more of a recreation/toy sort of thing.

If what you want is just something fun to scoot around on, then a scooter sounds like a great option. But otherwise, for a longer commute and/or real transportation needs, I would focus on an actual bike.

At your price point, you'll want to look at well-used bikes, and you might want to push the budget a bit so that you can accommodate some initial parts replacements to get a cheap bike back up to snuff. You can't get a great bike for that kind of money, but you should be able to find something that can get you from point A to point B more safely, and even more quickly, than a scooter could. Be prepared to do the bulk of the maintenance on the bike yourself to save money; this means that while you can afford to buy a used bike with various consumables that need replacing (tires, brake pads, chain, etc.), you should try hard to make sure that the wheels are at least straight, there's no major rust (especially no rust on the rims and spokes), etc. I.e. make sure the bike is fundamentally sound, even if in need of some TLC, so that you can handle the needed maintenance items yourself.

Anyway, that's my two cents, even if that does suggest your question is, at least to some extent, "opinion based". :)

Rear brakes are less useful than front brakes. On a bike, the rear brake is doing ~10% of the work, while the front brake is doing the other 90% of stopping a bike.

Assuming the scooterer isn't moving their body mass backward, then I'd guess braking split would be about the same. If they lower their head and stick the backside backward while braking, then the balance will improve but is unlikely to get to parity.

So I'd say the rear brake doesn't really matter that much, until that one day your front brake fails under need. If the front brake locks up hard on a scooter then you're going OTB at almost any speed. If it fails open, then you will need the rear brake to stop, or just coast to a stop with the aforementioned "get off and run" technique.

Upshot Get a scooter with two working brakes, not just one, like in Vladimir's excellent answer https://bicycles.stackexchange.com/a/71348/19705

I would suggest getting a bigger serious scooter. Those have bigger wheels and are faster and much more durable. They also have rim or disc brakes on both wheels, no tyre friction brakes.

Although they will cost more than 100 GBP, there are some budget options available (try second hand!) and they are still much cheaper than bicycles. For example, the entry-level Yedoo two costs around 140 GBP but gives you so much more performance. I am not suggesting this particular model or brand and I did not test it myself.

On the other hand if you need something truly small, it won't be for you and the folding ones cost more.