The short answer
Reprocessed tea is three different things in one category, so the match depends on which you bought.
Scented jasmine matches a lidded porcelain gaiwan, because the lid keeps the aroma in the cup.
Aroma is the entire product with a scented tea, and an open mug lets half of it go into the room.
A gaiwan of 100 ml at 90 °C is the standard way to brew it.
Gan pu（柑普）matches porcelain or glass, and it wants boiling water and a long steep.
One segment of the fruit brews several cups, and a 250 ml vessel is a sensible size.
Compressed pu-erh matches a gaiwan or a small clay pot, exactly as it does in the dark tea category.
A pick is needed for that half of the category and is useless for the other two.
A thermos is a legitimate match for gan pu, which steeps slowly through a thick peel.
Glass is the weakest match overall, since it holds heat badly and most of this category wants boiling water.
It is still the right choice for watching a jasmine leaf open, if that is what you enjoy.
Gaiwan covers all three, and it is the one thing to buy if you buy only one.
Why it matters
The category is defined by what was done to the leaf, and the vessel has to serve that rather than fight it.
Scenting puts aroma onto the surface of the leaf, and aroma is volatile and leaves quickly.
A lidded vessel slows that down, and a wide open one speeds it up.
Compression does something else again, since it makes the leaf slow to open and gives it a smell needing a rinse.
A vessel you can pour out of in 3 seconds is the one that handles that step.
Heat is the second thread running through all three, and it points in different directions.
Jasmine sits near 90 °C, and gan pu and compressed pu-erh want a full boil.
One vessel can serve both, since porcelain does not care what temperature you pour into it.
Clay cannot serve both, because it takes up the flower scent and keeps it for months.
A clay pot used on jasmine will make every later tea taste faintly of flowers.
That is the clearest example anywhere of why absorption matters.
The vessel either stays out of the way, or it becomes part of the tea.
Neutral is safe
Porcelain is the safe default across all three halves of the category, and glass is close behind.
Both give back nothing, so a jasmine tea tastes of jasmine and a cake tastes of the cake.
That honesty is what lets you tell real scenting from sprayed aroma, which is the main risk here.
Real scenting is still detectable at the 4th infusion, and sprayed scenting is usually gone by the third.
A seasoned pot would blur exactly the difference you are trying to taste.
Buy porcelain with a well fitting lid, since the lid is doing real work with a scented tea.
Check the spout pours cleanly, because a dribbling gaiwan costs you aroma with every pour.
Clay belongs to the compressed side only, and only after you know you will stay there.
Avoid anything sold as zisha（紫砂）for under twenty dollars, which is slip cast and tinted rather than hand built.
Warm an empty pot and smell it, and put it back if there is any chemical note.
Keep the money in the tea, since the gap between real and sprayed jasmine is far wider than any gap between vessels.
Neutral ware and a known maker beat a fine pot filled with an unknown leaf.
Building a habit
The useful habit in this category is buying from one maker and learning what their tea tastes like.
Use the same gaiwan each time, and the differences you notice will be the tea rather than the ware.
Fix the dose at 5 grams in 100 ml, and weigh it, since the pieces here are irregular.
A segment of gan pu varies between 5 and 10 grams depending on the fruit, and guessing is hopeless.
A scale reading to 0.1 g removes that variable completely.
Hold 30 seconds on a scented tea and longer on a compressed one, and smell the lid at every pour.
Note the infusion where the flower stops, since that is the measure of how the tea was made.
Rinse compressed leaf once before brewing, and discard that pour every time.
Clean the ware with hot water only, and dry it thoroughly with the lid off.
Scented tea leaves an oily film that turns rancid if the vessel is put away damp.
Smell the empty gaiwan before each session, since clean porcelain has no smell at all.
The habit is buying from a known maker, and the gaiwan is only where you find out.