Different appearance of \dots, \ldots in text and math mode in LuaLaTex + unicode-math (bug)?

Question

I get tons of warnings "Command \textellipsis invalid in math mode" after I have switched to LuaLaTex. The warning comes from the unicode-math package, which I needed to set the math font. If I use \dots or \ldots (\vdots is ok) in math mode, the appearance is different from the text-mode version and I get a warning. If I use PDFLaTex or don't use unicode-math there is no difference in appearance and I get no warning.

Is this a bug (or at least is something not correctly implemented)? The MWE illustrates the problem:

% !TEX TS-program = lualatex
% !TEX encoding = UTF-8 Unicode
\documentclass{article}
\usepackage[english]{babel}
\usepackage[utf8]{luainputenc}
\usepackage{unicode-math}

\begin{document}
Warning: $\dots$\\
Warning: $\ldots$\\
Warning: $\ldots$\\
OK: \dots\\
OK: \ldots\\
OK: $\vdots$
\end{document}

LuaLaTex output with unicode-math:

PDFLaTex output:

Answer 1

The luainputenc package should be loaded only with legacy documents, but never when the encoding is already UTF-8.

The package loads lutf8.def that has

\DeclareUnicodeCharacter{2026}{\textellipsis}

(which is an error, in my opinion, but it's another matter).