I (think) I want something faster than a Celeron. I'm basing that on 10+ year old info on what a Celeron processor is.
Well, it is always something to be careful about because at the low-end you don't always get the real thing, even when they name it "12th gen" or whatever, but in this case, you do get genuine 12th gen cores in the Celeron and Pentium models. This was
not true with 11th gen (they were all 10th gen!).
So, if we take the G7400 for example, it has single core performance (according to PassMark) that is superior to a 10th gen i5. Web browser performance tends to be more inclined towards single core performance than multi-threaded, so if you look at
TPU's benchmarks, for example, the i3-12100F outperforms, or nearly matches the i7-11700! That said, a low-end Celeron or Pentium
will be slower because of other reasons (like how they have less cache), but because of their lower clocks and no turbo, you can passively cool them much more easily. I'd also point out that if you're doing a lot of other tasks with the PC, at the same time, then it would be unwise to drop so many cores, but for a pure web-browsing machine 2 cores is plenty. Many low-end or SFF machines use mobile, or embedded CPUs that are way weaker than desktop CPUs and they cope fine. There are alternatives to NUCs like Gigabyte Brix and ASRock DeskMini.
By the way, just for the record, while under moderate load there's practically no difference between an ATX PSU and a PicoPSU, at very low load PicoPSUs are way more efficient than ATX PSUs. Part of the reason is that ATX PSUs use at least 4-6 watts just doing nothing. You do of course have very limited connectors and have to be careful about peak power (e.g. when you boot, or if an i3 has a turbo).