What an interesting topic!
First, I am careful about the premise of the question. “Currently, Ukrainians are moving away from Cyrillic.” How many Ukranians? Just a few, making a political point? Or a large number of people, including influential cultural leaders? Are government standards and laws specifying that Latin script should be used over Cyrillic script?
For what it’s worth, Wikipedia’s Ukrainian Latin alphabet article describes Ukraine as defining how to use Latin script for spelling Ukranian names in non-Ukranian texts, or as a future possibility for Ukranian texts, but not as a current reality.
Second, regarding, “Which version do we accept?”, my first answer is: “all of them”. The technology for labelling languages of text fields allows for cases where a single language can be written in multiple scripts. If you simplify, the labels treat them like two different languages.
Third, MusicBrainz typically advances in response to volunteers who are willing to make contributions. If there are translators who want to contribute translations of Ukranian in Latin script, great! If there are also translators who want to contribute translations in Cyrillic script, also great! The only caution is, having many fragmented projects with similar purposes may result in none of the projects progressing far enough to be useful. The volunteers might be happier with the results of their work if they all unify behind a single project. But in my opinion, that is really up to the volunteers.
The translations are managed on the Weblate platform, and Weblate’s documentation on language definitions says,
Weblate prefers two letter codes as defined by ISO 639-1, but uses ISO 639-2 or ISO 639-3 codes for languages that do not have two letter code. It can also support extended codes as defined by BCP 47.
The current MetaBrainz Ukranian translations seem to use the language code uk. Wikipedia claims that ISO639-1 defines uk as referring to the Ukranian language, as written in the Cyrillic script. Translation into Ukranian in the Latin script should use a standard code for that purpose, perhaps uk-Latn (by analogy with sr-Latn in BCP 47, 2.2.3 Script Subtag.
So, if translators would like to contribute translations for MusicBrainz products in Latin-script Ukranian, I would suggest working with Weblate to agree on a language code to use across Weblate for Latin-script Ukranian. Create new MusicBrainz translation entries using that language code. They will be in parallel with the existing translations in Cyrillic-script Ukranian using the code uk.