My strategy for sending and opening gifts
Friendship level goes up when you interact. Normally max 1 step a day, but more during some events or when you complete a weekly challenge with your friends. The most common interaction is opening gifts. Trading and raiding each count as their own interaction.
When you have interacted with each other, the friend gets a blue "halo" in the friend list. Friendship has already gone up for that day and cannot go up again until the next day.
You can send unlimited gifts, but only open 30 a day, 40 during some events or conditions. With up to 650 friends, opens are genuinely scarce, and it is pure waste to open from someone I have already interacted with when I could have opened from someone else instead.
That is also why I do not send gifts to those who have already interacted with me, even if they are "giftable". It would be a waste for them if they open a gift from me the same day.
My goal is to interact with as many friends as possible each day, but without unnecessary work. Below follows my routine, somewhat simplified:
Morning and day: sending
I search for "interactable&giftable" and send a gift to everyone shown, until the list is empty. When they open my gift, the same day or another day, it counts as that day's interaction, and I do not have to open their gift myself later (if they sent one).
Evening: opening what is left
In the evening I search for "interactable" and sort so that those who have already sent me a gift show up first.
When I still needed XP, I tried to open every gift that gave 50,000 XP or more during a raid hour with a lucky egg active, for double points. This is often called "syncing". I do not do that anymore, so be aware that I also open gifts like that on any day now.
Priority order
Since I cannot always send to everyone, and can never open everyone's gifts, I prioritize in this order:
- Friends who have not reached Forever Friends. An interaction still gives friendship level progress, with a lucky trade as my goal, remote or in person. The search string "friendlevel-3" means every friend up to and including level 3.
- Forever Friends with a Pokémon for remote trade. The friendship is already maxed, but I am happy to do a lucky remote trade. The search string "friendlevel5&!stale" means everyone at level 5 (Forever Friends) except the ones I have nicknamed "stale", see below.
- Forever Friends without remote trade. Last in line. They do not seem interested in remote trade, the friendship cannot climb any further, and I do not need more XP, so you could say the friendship has stagnated. I have given these an alias of "stale" so I can easily exclude them in the search string above. I try to contact them via Campfire, but rarely get a reply.
PS. If your item bag drops below a limit of five gifts, you get a refill after a short while so you have five in total. As far as I know, this refill can happen twice a day.