It's usually meant literally, but "tea" doesn't just refer to the drink, but refers to the meal known as tea. There are quote a few different types of meal called tea, depending on which country or which part of the UK you come from.
For example, there's "low tea", or "afternoon tea", usually a light snack such as sandwiches or eaten between 2pm and 5pm. Nowadays, this can also be a treat in a cafe or hotel with cakes, pastries, or scones and jam and cream. (See this book and this book.)
There's also "high tea", an early evening meal, eaten between 5pm and 7pm. This would be followed by a larger meal later on. Low and high refer to the height of the table where tea was eaten.
Tea can also refer to the main evening meal in the north of England, Scotland, Wales and Northern Ireland.
"Taking tea" is a common phrase for having this meal or snack or just sitting down to brew up, pour and drink tea; it is somewhat of a ceremony. For what it's worth, here's an Ngrams chart (and there's not much difference in shape between UK and US English):
"Children to compete for chance to
take tea with the Mad Hatter."
This clearly refers to the Lewis Carroll's Alice's Adventures in Wonderland where in chapter 7 the Mad Hatter is having a tea party. It's always six o'clock, and they're always drinking tea. There's bread and butter laid out as well:
'Take some more tea,' the March Hare
said to Alice, very earnestly.
'I've had nothing yet,' Alice replied
in an offended tone, 'so I can't take
more.'
'You mean you can't take less,' said
the Hatter: 'it's very easy to take
more than nothing.'
'Nobody asked your opinion,' said Alice.
'Who's making personal remarks now?' the Hatter asked
triumphantly.
Alice did not quite know what to say
to this: so she helped herself to some
tea and bread-and-butter, and then
turned to the Dormouse, and repeated
her question. 'Why did they live at
the bottom of a well?'
But as to the original question, the winning children would join the Hatter's tea party. There might be actual drinks and snacks for the children, or it could be meant that the winners would get to spend time with the Hatter.
An "incomplete summary" (or "partial summary") with a possible negative tone ("Kind of" means "incompletely" and "sums things up" means "summarizes [the topic at hand]"); to me, there seems to be a dissatisfied tone implied by the comment (that the summary is incomplete) that is also bundled with an expectation that the summary could have (or should have) been better somehow.
Regarding popularity, this isn't a phrase that I recall hearing or reading anywhere (although it's not entirely unfamiliar), so I don't consider it to be popular (I'm in Western Canada; there may be other places where this phrase enjoys frequent usage).
Best Answer
FTR,
Not really. Traditionally it is an "old-fashioned sounding" phrase.
The phrase has, let us say, "dignity" and "charm".
As Morton mentions, there is a Church Song "All things bright and beautiful."
Traditionally, you would use the phrase it for shop names such as - let's say -
And so on.
IF you use it for something modern or fun, like "All things gym" or "All things data": it's not really a parody, it's more just a slight twist.
The form "All things ___" is usually used for more old-fashioned, dignified things: it's rather cute, a twist, to say "All things disco" or "All things data". Not really a parody though. Just a slight smile.
It's not a misuse of grammar. It has a clear and direct meaning.
Consider a similar phrase to "All things _____": you will occasionally see shops named "The Compleat ____" (With that archaic spelling.) For example, "The Compleat Watchmaker" or "The Compleat Knitter". In this case it's a reference to an old book "The Compleat Angler." My point is that "All things ____" is a phrase that traditionally sounds, err, traditional - dignified - "old-fashioned". There are a couple of phrases like this in English, where you substitute in the word of your choosing.
{A more extreme, indeed openly humorous, example is "Ye Olde ____". So, "Ye Olde Bake Shop" and so on.}
Unfortunately I have absolutely no idea where "All things ____" originated. Perhaps, from the church song title, "All things bright and beautiful," which is a Victorian hymm (the epitome of Victorian hymms :) ), written in 1848.
Regardless of the origin, "All things _____" is, yes, a catchphrase in English.
Traditionally you'd put something dignified and old-fashioned in there (like "knitting," say): putting in something modern is just a slight smile, not a parody.