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# [Jelly], <s>&nbsp;42 38 34 33&nbsp;</s> 29 [bytes]

 5ȷɓ;8Ä:2,3‘ḍȧ"“Ƈ×“=%»ḟ0$ȯb@ð€

A monadic Link which yields a list of lists, each being either one of the lists of characters 'fizz', 'buzz', or 'fizzbuzz' or a list of the (integer) digits in the given base (so works fine beyond 62).

**[Try it online!][TIO-jsgmdgps]**

###How?

Note that 
\$\lfloor b÷2+1\rfloor\ = \lfloor b÷2\rfloor+1\$ 
...and 
\$\lceil b÷3+3\rceil = \lceil b÷3+2\rceil+1 = \lceil (b+6)÷3\rceil+1 = \lfloor (b+8)÷3\rfloor+1\$

 5ȷɓ;8Ä:2,3‘ḍȧ"“Ƈ×“=%»ḟ0$ȯb@ð€ - Link: integer, b
 5ȷ - 5*10³ = 5000
 ɓ ð€ - for €ach f(b,n):
 8 - eight
 ; - concatenate -> [b,8]
 Ä - cumulative sums -> [b,b+8]
 2,3 - pair literal [2,3]
 : - integer division -> [b//2, (b+8)//3]
 ‘ - increment -> [b//2+1, (b+8)//3+1]
 ḍ - divides? -> [fizzy?, buzzy?]
 “Ƈ×“=%» - list of dictionary strings = ['fizz','buzz']
 " - zip with:
 ȧ - logical AND -> [0,0], ['fizz',0], [0,'buzz'],
 - or ['fizz','buzz']
 $ - last two links as a monad:
 0 - zero
 ḟ - filter discard -> [], ['fizz'], ['buzz'],
 - or ['fizz','buzz']
 @ - with swapped arguments
 b - (n) to a list of digits in base (b) (say, [nb])
 ȯ - logical OR -> [nb], ['fizz'], ['buzz'],
 - or ['fizz','buzz']


[Jelly]: https://github.com/DennisMitchell/jelly
[bytes]: https://github.com/DennisMitchell/jelly/wiki/Code-page
[TIO-jsgmdgps]: https://tio.run/##AT4Awf9qZWxsef//Nci3yZM7OMOEOjIsM@KAmOG4jcinIuKAnMaHw5figJw9JcK74bifMCTIr2JAw7Digqz///8xMA "Jelly – Try It Online"