For instance I'm trying to use the mail framework mod to send mail with a gift, and I want to use something from Artisan Valley or Tea Time; how can I go about this? I don't usually see object IDs in these mods.
You also need to add them as dependencies to ensure that the mod wouldn't load without them installed.
For vanilla items, see Modding:Object data#Raw data on the wiki; the number at the start of each line is the item ID. Items from Json Assets are more tricky since their IDs are reassigned dynamically. You might need to ask the authors of Json Assets or Mail Framework about that. If you add mail using Content Patcher though, Json Assets has custom tokens you can use to get the ID for an item.