I don't like the other answers, so here I go.
Outside of PMD:GTI there has not been potentially gendering terms used for Meloetta. Meloetta is genderless in the games, but that does not inherently determine it's gender in canon (like with Lugia). Here's everything relevant that I have found:
Meloetta is a Pokémon that has a femininely anthropomorphic figure with musical bar-style streaks in its hair, quarter notes (crotchets) (♩) for its arms and hands and pupil-less eyes resembling whole notes (semibreves). It has a jewel on its forehead and a black headpiece that seems to be shaped like a treble clef, which doubles as an attached microphone such as one often used by singers. Its ovular head seems to be a third of its body's height and about half its height in width. In its Aria Forme, Meloetta has light blue eyes and flowing, wavy hair with light-blue ovals that resemble whole notes. In its Pirouette Forme, it has auburn hair that seems to be stylized in a high bun and red eyes. In both forms, its midriff and eyes match its hair. It is a gender-unknown species.
Meloetta may be based on a muse, a goddess in Greek mythology with the ability to inspire artistic creation. Meloetta may also be seen as a personification of music since its design has multiple references to musical notation: its headpiece resembles a stylized treble clef, its fingerless hands and slim arms are shaped after musical notes, and its hair resembles staff lines with bar lines.
Meloetta's Pirouette Forme resembles a ballerina wearing a tutu, with its "hair" curled up in a bun, or possibly the headdress worn by Nefertiti in her namesake sculpture. This form may also take inspiration from Spanish Flamenco dancers.
Its transformation between forms, particularly in Pokémon the Series, is reminiscent of a magical girl transformation sequence.
Meloetta may be a combination of melody, pirouette (a type of movement in ballet), operetta, and the Italian feminine diminutive suffix -etta.
And here's what I found for PMD:GTI in specific:
Meloetta: After defeating the Bittercold and clearing the Worldcore dungeon, it will appear in the player's Paradise. It will then ask the player to gather parts to build a Musical Paradise shop. After building the shop and changing the Paradise's theme, it will ask to join the player's team. Meloetta has two alter egos depending on its forme
I looked through the PMD:GTI dialogue, script and while Meloetta is talking between forms to itself(?) and referring to one another as "My Prince" and "My Princess", I believe that is to help the player differentiate between the two talking to itself, as each Meloetta, while being the same, has two distinct personalities. It's possible they picked the more masculine royal term for pirouette form simply because fighting/fighting type is typically seen as more masculine.
It is important to realize that masculinity doesn't necessarily mean a man and femininity don't necessarily mean a woman. While these terms are heavily gendered, that doesn't necessarily mean that Meloetta identifies with the gendered associated with the terms.
Unfortunately, I could not find anything in Japanese. I was hoping to find some dialog notes in Japanese, but I could not find it. I have skimmed through literal hundreds of PMDGTI playthroughs in Japanese, but I could not find one that obtains Meloetta, so unfortunately I cannot speak for the Japanese versions. Something to keep in mind is that sometimes the translations are weird with gendered things, as Japanese doesn't use a lot of pronouns. I am very curious as to what terms they used in the original; if anyone can find that, I can update this with an explanation of what's said and an interpretation.
Keep in mind, PMD:GTI isn't necessarily canon to Pokémon lore. Even if Pirouette forme is a male in that game, that does not mean it is a male in the rest of the Pokeverse.
Conclusion:
Meloetta, while genderless, has multiple references and is designed to be feminine in both forms. While being gendered with masculine terms in PMI:GTI, that does not mean that it is a boy, and despite it being designed incredibly feminine, that does not mean it is a girl, either. There has been no she/he pronouns used for Meloetta, and there has been no confirmed gender for Meloetta. TL;DR, Meloetta is just Meloetta.
Please help me find this in Japanese to expand upon this answer.
Sources:
Transcripts
Meloetta Bulbapedia Page
PMDGTI Bulbapedia
