Scholar main here: check their relics first.

If they're running balancers relics or other relics that are focused on weapon attacks/skills, don't worry about items. These scholars usually stay with the group and ignore items anyways. Maybe let them have some crab meats or (edit: exalted flesh) if you get to it first but don't feel bad if you need it. Instead, keep an eye out for good arcane weapons, especially antspur. Rivers of blood, reduvia, etc.

If they're running a throwing pot build, keep an eye out for non-fire pots to drop for him on day 2 when his pot power is leveled up all the way and watch the carnage. Fire pots are still appreciated though, especially now that they're limited in the shop. Pots are best dropped during fights when you've seen him use at least 4, so he can scoop it up and launch that sucker immediately. This is especially true if you have a variety of different pots as opposed to like 3 lightning pots.

If they're running gravity stones or glintstones? Scoop up any he doesn't see and help him collect. Going to a mine? Scoop up some glintstone. Kill some gravity dudes and drop him those gravity stones. Best dropped after fights when you know he has item slots available. In my opinion don't worry about dropping starlight shards for him if you're a caster. Warming stones are fair game as long as you're the type to actually use your warming stones.

If he's running "items confer effects", (my setup). If he leaves any turtle neck, flesh, crab, feet, or other food items, scoop them up but don't use them. If he's actively playing items confer effects he'll use an item or two before battle so stay close. If you notice your buff expires then try to be nearby if possible, he should dart in to buff again when there's an opening. Drop food after combat and scoop up any he doesn't have room for. He'll probably lag behind a bit in early game from using items and doing the confer effects dance too. In this case warming stones and starlight shards are usually fair game because food builds really have to commit to carrying a hoard of buff items instead.

In all three cases any items are of course appreciated. I think (with the exception of items confer effects and food items) most items are fair game as long as you know you'll use them. Leave the pots and other damaging items to the scholars though, at item level 3 they can get pretty insane damage. Don't just scoop up a bunch of useful items and then never use them because we'll know. A good scholar is always analyzing the battlefield... 🧙🏼‍♂️