I think this latter design pattern is what the m.2 6 sata cards do. It's typically something like an ASM1166 chip. (the example below) or a Jmicron equivalent.
They say the bandwidth far exceeds the individual SATA port speeds. But, there's little to no visible buffer on the card.
It's not an HBA, as much as a port "multiplier"
https://www.newegg.com/orico-pm2ts6-bp-pci-express-to-m-2-ca...
The ASM1166 is a controller. Check the datasheet [1]. Otoh, this thing [2] is a port multiplier with the JMB575 [3].
You don't need a lot of buffer to be an AHCI controller. You need enough space for the work queue that the driver writes, for write requests, you can have one sector sized buffer, DMA to fill it and then send it to the disk, but if you have two buffers, you can max throughput without doing anything fancy. For reads, chances are you'll be able to DMA out faster than the disk filled, two buffers is probably enough there, too.
So I don't know how much space you need for the command queue, but NCQ max is 32, let's say each queue entry is 256 bytes cause that's probably way more than enough. For each port, then you'd need 8k for the command queue, 8k for write buffers, and 8k for read buffers. Or a total of 144k of memory for a 6 port device... That's not a lot of ram to stuff into a controller ASIC.
Maybe you want a little more ram, in case the driver gets behind. You don't need extra buffers for writes... if the DMA is too slow, you just lose throughput, but no big deal, DMA will only be too slow if the system memory controller is very busy, and you can let the disk idle then. You might want to be able to fully buffer all reads, even if you can't DMA them out though. Then you don't have to worry about what happens if a read comes in and you don't have anywhere to put it. In that case, you'd have 8k command buffer, 8k write buffer, 32x4k = 128k read buffer = 144k per port, 864k for a 6 port device, still not enough that you need an external ram.
[1] https://www.asmedia.com.tw/product/45aYq54sP8Qh7WH8/58dYQ8bx...
[2] https://www.amazon.com/ChenYang-Function-Converter-Adapter-J...
[3] https://www.jmicron.com/file/download/893/JMB575.pdf