Green’s Dictionary of Slang

pooh-bah n.

also poo-bah, pooh-ba
[Gilbert and Sullivan’s Savoy Opera, The Mikado (1885), in which ‘Ko-Ko’ is ‘Lord High Executioner of Titipu’ and ‘Poo-Bah’ is ‘Lord High Everything Else’]

1. [late 19C+] an important person; also attrib.

2. someone or something that serves multiple purposes.

In derivatives

pooh-bahism (n.)

[1900s] the promotion of individuals on the basis of connections rather than ability.