Stack inserters and the first two inserter capacity upgrades require only mineral, mechanical and electrical science, yet they are locked behind 39 research items requiring chemical science (if I count correctly). Is this intentional?

My base (early chem science) is currently limited by train loading/unloading speed (unless I build multiple ore loading and unloading stations).

Boxing ore will help with inserter throughput. You get that earlier than stack inserters.

It requires ceramic to make, so you wouldn't be able to make it without some chemical science.

You get inserter 2 at the electrical science tier. It's definitely intentional that you don't get 2 tiers of inserter at the same tier of science.

Not all techs require exactly 1 of each science pack all the time. Sometimes they will use 2 of something, or zero of something. Buffering science packs can be useful to smooth out production. When you research something that doesn't require a particular pack you can save it up so you don't slow down when you encounter one that requires 2x of that science.

Inserter 3 doesn't require any new chemistry breakthroughs to develop, but that doesn't mean that it doesn't build on any of the earlier technology that does require new chemistry.

There are 2 logistics mods included in both official Nullius mod packs that could help you here. Bulk Rail Loader and Miniloader.