Honestly, if we are going to get presents, we really should be looking at Panoramia the woman, not Pan the abstraction of a jade wizard that we happen to be dating. So what do we know about her personality?
We know she is daring. Her first move in her journey was to join a military expedition against the undead of Mordheim, putting her directly into a hot military conflict that sounded like it got rough. Then she followed up by joining an expedition across the old world to do it again.
We know she is idealistic- she knew who we were and was excited when she met us because of what we represented, and she refused to avoid battle when her friends were getting stuck in even at personal risk.
We know she is cheerful and friendly, from how she makes friends wherever she goes and the way she interacted with the ducklings when they were new.
We know she is observant, from the way she picked up on waaaghsoak shrooms and saw through our facades, and is more enthusiastic than offput by hard, dirty work.
More relevantly, we know she is frustrated with the jade college and it's preoccupation with gods instead of the deeds she focuses herself on, and we know that it was the environment she grew up in, making her determination to get out and stay out suggestive of a willingness to burn bridges and make a stand on her principles.
And with this last update, we know she is quiet and comfortable spending time being scholarly, and her idea of 'not doing anything' is much more related to not being out in the fields working than not actually doing anything.
What does she like? I'm betting that clever things and trinkets arent much her area, and she does not at all seen like a party girl despite the halfling's reputation in that area. Probably like Mathilde in that she likes wizards and other species more than humans, but I bet a lot of that is due to growing up in the colleges and only getting scary stories second hand.
She does not seem to be like a shallayan, looking to care and nurture, but rather more like Gotri in that she likes to tinker worth things and see the results, to build stuff and be radical.
So my bet on presents for her would be mundane tools, or an enchanted book that can survive dirt and water to retain what she writes on it, or new things that are outside the experience of the jades back in Altdorf.
I would argue against adornments for appearance, or weapons, or replacements for things she already has.
But I bet the best things we could do for her are to be a showman and a mystic for her, to pull her in to our side of the curtain and show her worlds she would never have seen otherwise.
Like, the both of us wearing mutable visage to an Altdorf noble party, or the caverns of Vlag where they grew their underground food, or the elven forests.
Bring her into our secrets! Maybe swing through the royal zoo and on the way introduce her to our good friend the empress, and our godson.