\documentclass[a4paper]{article}
% \usepackage[greek,english]{babel}  % babel-greek
\usepackage[greek,english,provide=*]{babel}    % Babel's Greek "ini"

\usepackage{parskip}
\newcommand{\langGreek}{\foreignlanguage{greek}}
% \renewcommand{\langGreek}{}  % check without language change


\ifdefined \UnicodeEncodingName
  \usepackage{fontspec}
  \setmainfont{FreeSerif}
  \newcommand*{\texengine}{Xe/LuaLaTeX}
\else
  \usepackage{lmodern}
  \newcommand*{\texengine}{pdfLaTeX}
\fi


\begin{document}

Greek question mark:
\langGreek{; → \MakeUppercase{;}}

Latin accents: 
\langGreek{ᾰ Ᾰ ῐ Ῐ ῠ ᾱ Ᾱ ῑ Ῑ ῡ → \MakeUppercase{ᾰ Ᾰ ῐ Ῐ ῠ ᾱ Ᾱ ῑ Ῑ ῡ}}

hiatus:
\newcommand*{\hiatest}{άι, άυ, έι, ἄι, ἄυ, ἔι, ἀυ}
\langGreek{\hiatest{} → \MakeUppercase{\hiatest{}}}

\langGreek{ἀυπνία → \MakeUppercase{ἀυπνία}}

Spacing prosgegrammeni:
\langGreek{ι → \MakeUppercase{ι}}

Spacing accents:
\langGreek{῀ ` ´ ῾ ᾽ ᾿ \quad  ῍ ῎ ῝ ῞ ῟ ῏ ῭ ΅ ῁ → 
  \MakeUppercase{῀ ` ´ ῾ ᾽ ᾿ \quad ῍ ῎ ῝ ῞ ῟ ῏ ῭ ΅ ῁}}

Eta with tonos:
\langGreek{ή, Ή → \MakeUppercase{ή, Ή}}.

\end{document}

Upcasing/downcasing literal chars of the "Greek and Coptic" and "Greek
Extended" Unicode block now works without errors.

Problems (in order of urgence):

* Uppercase of character 0x37E GREEK QUESTION MARK is 0x3B SEMICOLON which is
  mapped to a middle dot (0x387 GREEK ANO TELEIA) by LGR:

* The “educational”/“Latin” accents *macron* and *breve* (*vrachy*) should
  be kept (they stay above capital letters similar to the dialytika,
  they are kept by Apostolos Syropoulos' “xgreek” package and in babel-greek
  “since ages”):

* Auto-Hiatus also required after
  0x1F00 GREEK SMALL LETTER ALPHA WITH PSILI + iota or upsilon.

* Spacing prosgegrammeni turned to capital Iota (kept as prosgegrammeni with
  old MakeUppercase).

* Spacing 0x1FEF GREEK VARIA becomes 0x2018 LEFT SINGLE QUOTATION MARK
  (visible difference with XeTeX and DejaVu),

* Non-uniform handling of spacing diacritics: Single diacritics are kept,
  combining diacritics are mapped to single diacritics.
  (The old implementation handled spacing diacritics similar to
  diacritics in accented letters.)  

* How to treat MakeUppercase of a single captial GREEK CAPITAL LETTER ETA
  WITH TONOS? Currently, it is treated differently from the small
  equivalent.
