That is because \[Alpha] is not a symbol, it is a named character. Programatically (from here)

Select[Table[{#, ToString[FullForm[#]]} &[FromCharacterCode[i]], {i, 65535}], StringMatchQ[#[[2]], "\"\\[" ~~ __] &]

search all entries which including a substring expressed by a specific regular expression from the above output

All symbol names with 4 uppercase characters

allSymbols // Select[StringMatchQ[CanonicalName@#, RegularExpression["([A-Z].+){4}"]] &] 

But I still can't figure out how to enumerate each command and symbol as a parameter and feed it to WolframLanguageData.

The first example in the Details section

WolframLanguageData[] gives a list of all Wolfram Language symbols.

allSymbols = WolframLanguageData[];
AssociationMap[#["DocumentationBasicExamples"] &, RandomSample[allSymbols, 5]]

But there is no official Wolfram LSP client for Emacs.

Right. Emacs does support LSP so you could write one using the existing languages Emacs supports and the official ones for Visual Studio and Sublime as examples.