SCPI is a standard that defines a common communication protocol with common commands. This way instruments from different manufacturers are compatible with the same test automation scripts (well.. sometimes not entirely in practice, but it does make it much easier to port to a different instrument)
The SCPI standard defines that human readable ASCII is used for both commands and data. This is then sent over whatever communication link is being used to the instrument. These links operate similar to a serial port. Be it the original IEEE488 GPIB it was originally made for, more modern USB, RS232, a TCP/IP connection over ethernet..etc. So when you send a SCPI command it is just ASCII being sent byte by byte to the instrument over your communication link flavor of choice. Instruments can implement non ASCII formats too, but those commands are not really SCPI anymore, they are just a manufacturer proprietary command.
This kind of protocol is designed to be simple and easy to use (hence human readable ASCII for everything), not performant. As such the whole architecture around it that runs is is not built for high throughput or low latency. In the instrument this is typically handled by the main CPU that also runs all of the UI, so it has a limit to how much CPU time it can dedicate to the task of SCPI parsing and needs to actually fetch data from elsewhere (like in a scope, the acquisition ASIC/FPGA), so even when using the proprietary binary format commands you don't get great throughput.
What you will generally get with oscilloscopes is being able to capture up many points (up to the max sample memory of the scope), then send those points over SCPI and start a new capture. So there will always be at least a small gap between where one capture ends and next starts.
So scopes that can do live streaming will usually move data over some more proprietary protocol that is built from the ground up for high throughput. Often the motivation to put work into implementing that is that the scope can use the PCs system RAM as giant sample memory.
The real solution for high speed real time continuous signal capture into a computer are so called digitizer cards. They are purpose built pumping data from an ADC into a very fast PCIe bus:
https://www.keysight.com/us/en/products/modular/pxi-products/pxi-oscilloscopes-digitizers.html#DynamicTable(But is a rather expensive solution as you might imagine, so best to go for a cheep USB PC based scope that has some continuous streaming API documented)