if it were twice the height then perhaps a serving rummer, but it's not, although in my opinion I think that's the nearest it comes to a drinking related item - and I'd agree with Christine that the water staining is probably the result of being used as a vase. It's amazing how many unrelated, antique pieces, are commandeered as vases that were never intended as such. As far as I know, tea mixing was a dry process.
I believe caddy bowls were sometimes heavily cut and decorated, despite being hidden with the caddy for most of their lives.
My own thoughts on these things are.............. straight parallel sides, with some reasonable height, probably indicates a tea mixing bowl, and they do seem to come with feet, despite the snug fit in the caddy suggesting otherwise. Quite why some should have extensive wear under the foot doesn't seem immediately obvious.
Pix one and two show what I think are possibly all mixing bowls - cut and pressed.
Picture three shows what I believe are sugar bowls - less height, curved sides and with a foot as you'd expect.
Those sugars with a pedestal/stem are very obviously sugars, but care needed to differentiate between them, and comports, which are similar but with a much shallower bowl.
The last picture shows two pieces about which I'm uncertain, although I'm tempted to think mixing bowls. They are a little shorter than the mixing bowls in pix one and two, but their profile doesn't have the curve of a sugar.
When you think of the variation in these items, it surprised me to find that I have two identical examples of the last one showing the pteridomania engraving which date to around the middle third of the C19. I'm tempted to think the other piece in the same picture is probably a little older.
But I'd agree that it's not always obvious which is a mixing bowl and which is a sugar.
I'm not sure what sort of implement was used to mix the dry tea - presumably metal. As for sugar, presumably after about 1840 tongs were used to serve lump sugar. Can anyone add some accurate details here ... when did the need for sugar cutters end and lump sugar take over from chopping lumps from a cone?
Unfortunately, mixing bowls appear to have less book coverage than just about anything else, and I couldn't find anything of use, so the above are my opinions rather than facts. If anyone knows of a good book, please shout.