Instruction Sets are not necessary CPU features. For example, Hyperthreading is not part of any instruction set, but is rather a CPU feature which allows a single core with two execution units to be perceived to the system as if it was two cores.
All Versions of Windows 2000 would interpret a CPU with Hyperthreading as two logical cores. The issues surrounding Windows 2000 and hyper-threading are because Windows 2000 didn't know that it was actually a Virtual core, and as a result treated it just like a logical CPU core. This caused performance degradation, in general, because the two "Cores" were really just separate execution units which shared a lot of cache and prefetch information.
The problem you saw (where only one CPU was visible) was because the HAL was still the single-processor HAL. You can change that as documented
here. I believe Windows XP might have similar requirements.
This hyperthreading issue was fixed with Service pack 5 of Windows 2000 and both the Home and Pro Versions of Windows XP understand virtual cores and will schedule processes and threads differently based on whether they are virtual or logical CPUs and what logical Cores a virtual core is tied to in order to improve performance. Generally, Operating Systems only add "support" for CPU Features when it actually affects how the OS or the Kernel should function. For example, Hyper-threading is "supported" in the sense that the Kernel now needs to consider differences between Hyper-threaded "virtual" cores and actual CPU cores when it comes to scheduling thread affinity or face a significant performance penalty.
Support for Instruction Sets such as SSE/SSE2/MMC etc. tends to fall on individual programs. MMX instructions, for example, aren't very useful for a OS Kernel to support, since they are designed for Multimedia features. Any program running on a MMX-capable CPU can use MMX instructions as long as the CPU is operating in a 32-bit mode or a 32-bit compatible mode. Certain instruction sets require different Operating modes.
By that token, an Operating System's "Support" for instruction sets is really just determined by what CPU mode it operates in. In the case of Windows XP (excepting the special x64 version) that means 32-bit protected mode. This means that software running on the OS can use any 32-bit instruction set supported by the CPU, but even if the software supported it, it would not be able to execute any 64-bit instructions.
For example, in the case of the Sempron, it is a 64-bit CPU. Since you would be running XP, Every single 64-bit instruction set is "off-limits" because it requires 64-bit Long mode. According to the specsheet it supports MMX, MMX Extensions (Multimedia Extensions Extensions... heh...) SSE,SSE2,SSE3,SSE4/4.1/4.2/4.3,AES,AVX,BMI1,F16C,AMD64,EVP,AMD-V and likely a few others. many of those likely require 64-bit Long Mode in order to function, and some may have functionality that is only present in 64-bit modes. Any of that functionality will be locked out to you and any software you run if you are running a 32-bit OS.