It looks like some of the characters can only be exported to $\TeX$, but not imported. TeXForm[\[HBar]] results correctly in \hbar, but ToExpression["\\hbar", TeXForm] gives \[Null].
Let's try finding other characters that have the same problem. Because some characters work as unary or binary operators, we will also try importing them as $\alpha \; \square \; \beta$.
$Version (* 13.3.0 for Microsoft Windows (64-bit) (June 3, 2023) *) Grid[#~Join~{TeXForm[#[[1]]], Quiet@ToExpression[ToString[TeXForm[#[[1]]]], TeXForm, HoldForm], Quiet@ToExpression[ "$\\alpha " ~~ ToString[TeXForm[#[[1]]]] ~~ " \\beta$", TeXForm, HoldForm]} & /@ Select[Table[{#, ToString[FullForm[#]]} &[FromCharacterCode[i]], {i, 65535}], StringMatchQ[#[[2]], "\"\\[" ~~ __] &], Frame -> All]

We see that quite a few characters can be exported but not imported.
TeXForm[\[HBar]]results correctly in\hbar, butToExpression["\\hbar", TeXForm]gives\[Null]. I am using13.3.0 for Microsoft Windows (64-bit) (June 3, 2023). $\endgroup$