13kg is quite small for a 3yo. (Not that this really matters, in fact in terms of car seats, small tends to be an advantage!) Do you know his height? That will be more relevant for some of the seats, as many go by height now.
If you definitely want the seat to last until 12, then honestly I'd look at forward facing, (the seats which forward face and include both harness and booster mode are called 123 seats) but it will be a step down in safety now. If you want to prioritise safety now, then rear facing is the best choice.
Consider the fact that you'll need to hand the seat down again anyway, and the fact that combination harness + booster seats are used longest in booster mode, it makes some sense to prioritise a well rated, practical, easy to use booster seat when the time comes - the combination ones are usually less well-rated for safety, and in practical terms they tend to be bulkier and heavier. High backed boosters need not be expensive, it's the harnessed phase which is expensive. You can frequently find a very well rated HBB for under £100, sometimes as little as £50-60 (though this is less common.) It's quite possible that cheaper, safer HBBs will become more prevalent as the cheaper brands also move over to the newer regulation.
So you could look at another spin seat, which will probably last your 3yo another 18-24 months depending on their height. This is probably your least favoured option because both seats will be outgrown at about the same time and you'll need to buy 2x high backed boosters long term. But it's cheap - you can get spin seats for as little as £150-200 from decent brands, or spend around £300 for a luxury one. Also, you know the seat works for your car and child.
There are spin RF/FF seats which also have a booster seat mode like the Silver Cross mentioned, but there are some downsides to these - they tend to be very bulky and heavy, they can usually only rear face in reclined mode, which means they take up more space and some toddlers won't like this. The Silver Cross itself is expensive (about £400) and the safety rating of it is around the same as a good 123 type seat. Because these seats have so many modes the safety score is averaged between them, so you can assume that the rear facing mode is safer than a 123 seat, but a bit worse in comparison to RF in a spin seat without booster, like your Joie. When you convert it to forward facing, whether harness or booster the performance is likely to be a bit worse than it would have been if you'd gone for a well rated 123 seat or standalone high backed booster seat. It's not bad, though, the Silver Cross one did well in this category. With this category (multi stage/all stage) in general, the seats tend not to do as well - the Silver Cross was a bit of an outlier, so personally I wouldn't look at other brands. In particular, there are a lot of extremely cheap seats in this category around the £150 mark which should be avoided. In terms of handing down, one child could stay in this seat as a HBB seat and the other will still need their own HBB seat. But as mentioned, these aren't the easiest seats to move around and once in HBB mode you might be tempted to abandon it for something smaller and lighter. The other thing is that if either child is tall, you may find you end up needing to buy a larger harnessed seat to tide them over in the middle.
So another option to continue rear facing would be to look at the Swedish type ERF seats which rear face up to 23/25kg - this would basically mean you can use this as long as you like until the youngest needs to move out of the Joie 360. The safety of them is world-class, can't be beaten. They start at about £250 - Axkid Move is currently £200 in a sale. There are a couple of isofix models available, lightweight, easy to swap around, priced at £450 for Joie i-Prodigi, or Axkid One2 is on offer for £550, usually £650. If your 3yo is average height, any of these will probably last him until roughly 6/7 years, longer if his height is in proportion with weight. Then you'd need to purchase a high backed booster seat to last him until age 12, with your youngest able to move into the 25kg+ ERF seat until they are 6/7 years old by which time your eldest will be 9-10 and you could judge at that time whether they are tall enough for no car seat or a backless booster.
The forward facing option covering now until 12y would be something like Britax Advansafix or Recaro Tian elite or Maxi Cosi Titan Pro i-size (the latest version did well, earlier versions of this didn't have such a great safety rating). You need top tether to fit the majority of these seats, which is either easier or massively more hassle depending on your preference. 🤷♀️ I find it easier than wedging myself in the footwell with the Joie 360 Spin, but DH hates having to go back and forth into the boot to tighten the tether. Top tether tends to mean lighter/less bulky, especially compared with spin seats, but they are heavier than the Axkid One/Joie i-Prodigi. You will also see Joie Bold recommended, because Joie Bold has a higher harnessing capacity - up to 25kg. Assuming your 3yo is average or smaller height rather than a beanpole, you probably won't need the extra harness capacity of Joie Bold, so my preference would be one of the above mentioned models which have a better safety rating. You will still need to buy 1 more high backed booster for the other child. Sometimes the 123 seats are shorter as a high backed booster compared to standalone high backed boosters, which doesn't matter so much with a 3 year gap.
Sorry that was long - I think overall, I'd say either a well-rated 123 seat OR a 25kg+ Swedish ERF seat would be my vote for you, but the Silver Cross might work too.
+1 for 123 seat if you are happy to FF 3yo now in return for keeping both kids in good HBB longer term.
+1 for 123 seat (or Silver Cross) if both kids are average height or shorter
+1 for ERF seat if you want to maximise RF time for both kids
+1 for ERF seat if you don't mind buying 2x HBB later, or graduating eldest to booster cushion at 9/10
+1 for ERF seat if either child is over average for height
+1 for Silver Cross All Size if you want the combo of RF + use until 12, and don't mind the downsides.