Short answer: 'amount' with countables may be seen as idiomatic or informal. You can't go wrong if you abide by the standard 'compact dictionary' or learner's 'rule' that 'number' is for countables and 'amount' is for non-countables, especially in school tests, etc.
Long answer: the noun 'amount' is usually restricted by dictionaries to uncountable or mass quantities, but Britannica, which you have quoted, is not so dogmatic ('chiefly', 'sometimes', and 'often criticized as an error'). Oxford Advanced Learner's Dictionary also:
(used especially with uncountable nouns)
Amount is most often used with uncountable nouns:
an amount of
It is also sometimes used with countable
nouns, especially in spoken or informal English:
You're competing with a massive amount of people.
However, some people consider
that this is not correct and prefer to use number with countable
You're competing with a very large number of people.
Amount (Oxford Learner's Dictionaries)
Note that when a dictionary includes qualifying words like 'often', 'chiefly', 'mainly', 'sometimes', etc, it is providing a usage note or definition that is not totally exclusive, and may be descriptive rather than prescriptive; exceptions may be found in real-world use.
Compare with 'less' and 'fewer'.
Fewer versus less (Wikipedia)
The Oxford English Dictionary also:
4.4 In colloq. phr. any amount (of), a great deal (of) (cf. any a. 2 b); no amount of, not even the greatest possible amount of (orig.
1893 G. B. Shaw Widowers' Houses ii. iii. 41, I have any amount of
letters for you. 1914 M. Sinclair Three Sisters lxiii. 369 And he
had spent any amount of money on it. 1921 E. O'Neill Emperor Jones
v. 185 Capable of any amount of hard labor. 1925 F. Scott
Fitzgerald Great Gatsby v. 116 No amount of fire or freshness can
challenge what a man can store up in his ghostly heart. 1952 G.
Sarton Hist. Sci. I. xiv. 363 It takes a surgeon to appreciate the
fine points of Hippocratic surgery, and no amount of explanation
would help other readers to judge them correctly. 1961 N. D. Gill People
of Way v. 55 Many people wake up tired of a morning and no amount of
rest seems to make any difference. 1961 D. Black Foot of Rainbow
xxviii. 199 There was any amount of drink on board. 1968 Listener
10 Oct. 472/3 ‘Did you encounter opposition in the early stages?’ ‘Oh,
any amount.’ 1973 E. F. Schumacher Small is Beautiful i. ii. 33 The
disease having been caused by allowing cleverness to displace wisdom,
no amount of clever research is likely to produce a cure. 1985 N.Y.
Times 18 Dec. d27/6 When you can get five goals on thirteen shots,
that pretty much makes up for any amount of mistakes.