The best they should have done is instead keeping their existing keyboard layout, continaing both the Cyrillic letters and Latin QWERTY printed on them, but operating in two modes (depending on OS preferences) to invert the two layouts but without changing the keystrokes. It would just have needed one Latin letter or modified Latin letter so that it was simply a 1 to 1 transliteration. No need to type an extra apostrophe. No extra dead key was needed to remap to Latin the few Kazakh Cyrillic letters that are already typed with AltGr (the labels for them are on the bottom right of the key, with no character labeled above it, so it was also possible to use the upper position to indicate the associated Latin letter: when turning the keyboard to Latin mode instead of Cyrrilic by default today, the position of letters do not change, the labels are still valid where they are but AltGr will render the Latin key labeled at the upper position. All existing keyboards would remain usable as is. Users would then choose the Latin or Cyrillic layout as they want and could still switch from one to the other. Note that the placement of Cyrillic letters on the QWERTY layout of Latin letters is not from a direct transliteration: the paired letters do not match, but it does not matter (mapping keys on keyboards is not nessaraily a transliteration), but the existing Basic Latin letters A-Z should remain where they are on the QWERTY layout. The other Cyrillic letters are on keys that won't move but that will have the additional Latin letters needed for the language.
Note also that there are two Kazakh-Cyrillic layouts, including one where the most common punctation (:,;.) are on two keys in the middle the 1st row (digits are typed using AltGr or with the numeric keypad): this layout also should not change, and the same two keys will keep these punctuations. But here again there's a single keystroke for each Cyrrlic letter, on the other keys, that will also keep the QWERTY layout of the Latin letters in their alternate mode. Only Cyrilic letters on other keys of the 2ns, 3rd and 4th row will need to map the missing non-basic Latin letters neededn alkso typed now with a single keystroke when the keyboard is turned to Latin mode. In all cases, the Latin keystrokes should also generate only one character only, not digrams. And its possible to use "correct" extended letters even if this requires some minor adaptation of existing transliterations (that use more complex rules with digrams), and it was perfectly possible to use Latin letters with acute accents for vowels, or with carons for consonnants, or possibly the cedilla below s or c, for every Kazakh Cyrillic letters to reach that goal without difficulty: a non-ambiguous, simple 1-to-1 transliteration, fully reversible, allowing also all historic texts in Cyrrlic to be transliterated instantly without loss, and still allowing clear reading of the Latin text, easy composition. Unicode (but also legacy ISO 8859 and Windows or MacOS codepages for Eastern European language in Latin) already support all the needed extended Latin characters.