I have green science unlocked, but my whistlestop assembler does not let me select the recipe for it. I do have a host of mods installed. Most are QoL mods. Some are minor additions, like true nukes, deadlocks stacking beltboxes, deadlocks crating machine, and beautiful bridge railways.

Can you make green science in regular assemblers in your mod pack? Giant assemblers can only make assembly things (and a few bobs things if you have that mod). None of the mods sound like they effect where science packs should go. You may have done something weird like loaded some mods later or relating to upgrading mods at weird times mid game.

WARNING: Any console commands you try will disable achievements for your save. Also, you should back up your save before trying any of these.

I think you may need to reset things to get it to work (especially if you find starting a new game and typing /cheat all in console and see if assemblers are still broken there). Its been a couple years since I did any factorio lua, so I don't recall the command but I think /c game.player.force.reset() might do it, though that may also bring your technologies back to square one? I don't recall.

The other resets to try are
reset_recipes()
Load the original version of all recipes from the prototypes.

reset_technologies()
Load the original versions of technologies from prototypes.

reset()
Reset everything.

reset_technology_effects()
Reapplies all possible research effects, including unlocked recipes.

I think the plain reset is just a combination of the other three.

The thing can be manufactured in an assembler I place down. And reset_technologies of course, killed all of my research. If I researched the technology again, perhaps it would show back up, but I didn't want to.

reset_technology_effects() resulted in the big factory having the desired recipe.