-- INFORMAL --
do:
take (a narcotic drug).
"he doesn't smoke, drink, or do drugs".
https://www.google.com/search?q=define do&rlz=1C1NDCM_enUS84...

Since tea is addictive, it is a mild narcotic drug.

I'm just guessing, but doesn't the above phrase "Mrs. Edwards have never done tea", means she is not sociable so she will not participate in drinking tea with other people? The word "tea" in terms of slang means to gossip, so maybe she's not the type of person who would engage in meaningless gossip stories with other people.

https://www.dictionary.com/browse/tea

"‘Tea’ per definition means the following: 1) Tea, the beverage made by infusing dried and crushed tealeaves, or by mixing pulverized tea leaf in hot water, consuming the leaf in its entirety. 2) The tea leaf obtained from the Camellia Sinensis – an evergreen shrub also known as the tea-plant – of which the youngest buds and leaves are plucked and then heated and rolled/crushed to dry. 3) The act of brewing, serving or consuming tea; ‘to do tea’ (emphasis added). Which in extended meaning can also be used to refer to the rite of tea." https://www.the-tea-crane.com/blog/japanese-tea-types-chart/

While the British may have perfected the "art" of tea-drinking, the tradition actually comes from China. The Portuguese word for "tea" is "chá", which derives from the Chinese.

"The etymology of the various words for tea reflects the history of transmission of tea drinking culture and trade from China to countries around the world.[1] Nearly all of the words for tea worldwide fall into three broad groups: te, cha and chai, present in English as tea, cha or char, and chai. The earliest of the three to enter English is cha, which came in the 1590s via the Portuguese, who traded in Macao and picked up the Cantonese pronunciation of the word." https://en.wikipedia.org/wiki/Etymology_of_tea

cha: noun Tea; -- the Chinese (Mandarin) name, used generally in early works of travel, and now for a kind of rolled tea used in Central Asia. (...)
In Ireland, or at least in Dublin, the term "cha" is sometimes used for tea, and "char" was a common slang term for tea throughout British Empire and Commonwealth military forces in the 19th and 20th centuries, crossing over into civilian usage." https://www.wordnik.com/words/cha

The customary indulgence in afternoon tea-taking had never been a habit to which Mrs Edwards subscribed. Popular from Georgian-Victorian times, it's still a well-known and widely indulged in habit today, whether by workers slurping tea from pint mugs in factory canteens, or company directors taking theirs in fine china, or to the Women's Institute all sticking their little fingers out whilst drinking theirs alongside munching daintily on finger, crust less sandwiches and Victoria sponge cake and fondant fancies, things haven't changed much. As far as Mrs.Edwards was concerned, it was just a habit she observed others indulging in, while giving it a wide berth herself.

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Note added at 9 hrs (2024-02-11 18:41:57 GMT)
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...and of course, as a wealthy woman of status, her abstinence from the habit would have been noteworthy amongst her peers;

i.e. she "has never done with tea"
Only a guess as the grammar doesn't really fit with this

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Note added at 11 hrs (2024-02-11 20:55:09 GMT)
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This is ONLY A GUESS