The Solar Locomotive is not in the same fast-replace group as other locomotive tiers. This makes it impossible to automate replacing regular locomotives with solar locomotives.

Several things. First of all they're all specified with the same fast_replaceable_group value of "locomotive". It's in the prototype, but I just verified it in game to make sure no other mod is messing with it, by using the following command:
/c game.player.print(game.entity_prototypes["nullius-solar-locomotive"].fast_replaceable_group)

Though the game engine doesn't seem to support fast replacement of trains, so I'm not sure this field is actually being used for this. They are set to the same group, but I don't think that's relevant.

Automating the upgrade of trains is the whole reason that the Train Upgrader mod exists and is included in both of the official Nullius mod packs (Momenti and Maximus). I've tested it before, and just double checked now. I wrote the Train Upgrader mod myself, so this is precisely what it's intended to work for. With the Train Upgrader mod and Nullius, I can upgrade a Locomotive 1, 2, or 3 into a Solar Locomotive, or I can upgrade a Solar Locomotive into a Locomotive 3, using the Train Upgrader station. Make sure you read the mod page for that mod and know how to use it correctly. Train Upgrader doesn't actually check the fast replaceable field, so that's not what makes it work here.

If you still can't get it to work, is it possible that you have some obscure, unsupported mods that could be changing trains in some way? Train Upgrader will only upgrade trains if they match in their physical dimensions, and an incompatible equipment grid could also be an issue. By default Nullius declares these trains to be compatible, but some other mod could interfere with that. Try hovering over the locomotive and see what mods it reports as modifying them. For me, when I have Nullius Momenti installed and hover over Locomotive 3 and Solar Locomotive, both say "Nullius > Shuttle Train Continued", indicating that the Shuttle Train Continued mod has done something to modify those entities (add an equipment grid), though it doesn't make them incompatible with Train Upgrader. If in your game it shows some other mod has modified one or both of them, that could be the culprit for what's making them unupgradeable.

Solar locomotive's entity mod list only reports: "Nullius".

I had successfully used the Train Upgrade Supplier before to upgrade tier 1 locomotives to tier 2 locomotives (though there were some... Interesting trials in getting that to work in a non-disruptive way) so I'm not sure why I'm having difficulties doing the tier 2 locomotives -> solar locomotives upgrade.

https://cdn.discordapp.com/attachments/486240041094348838/1127350668236161127/image.png

I also tried putting the upgrade upgrade supplier north of the train stop, but to no effect.

After some tinkering, when I ticked the enable train limit checkbox, a train suddenly appeared in the list of trains with this stop. Except with a limit of 0, that train said the destination is full and did not come. If I changed the limit to a reasonable number (5), the train disappeared from that list. Unticking and re-ticking the box assigned a different train to this schedule.

(Working without train limits was what what made it a challenge to upgrade locomotives non-disruptively previously in this playthrough.)

Edit: Turns out the signals on my stacker were on the wrong side. Trains could not path to the station so did not come to get upgraded.

Alright, thanks for the update. So it sounds like it's not a problem with the mods, which is good.