I'm not Matt but, if these are standard on the version you intend to buy, yes it *should be noticeably faster.
The MINISFORUM NPB7 Mini PC is equipped with Intel 13th Gen Core i7-13700H(14 cores/20 threads/up to 5.0GHz) Processor. With Intel Iris Xe Graphics eligible (the graphics frequency up to 1.50GHz), it offers an excellent performance of Internet and Office applications, Monitors, Projects and TVs.
This Mini Computer comes with DDR5 16GBx2 memory + M.2 2280 1TB PCIe 4.0 SSD storage (up to 2TB).
Though your previous computer did have an SSD hard drive (which is fast), M.2 is supposed to be even faster .. plus you appear to be getting 8X as much hard drive space and many more processor cores/threads and better speed ..
It doesn't specify NVMe (which makes these M.2 drives even faster), just how much faster could be arguable .. could be marketing not mentioning it or intentionally hiding it .. but still likely faster and larger storage than previous machine
Oh wait! it does mention PCIe 4 .. so yes, it should be a fast machine for your intent .. NVMe might be overkill for your needs (and cost more)