Languages don't come from stats, ability scores, or skills. They come from race, and possibly from class or background.
Languages
By virtue of your race, your character can speak, read, and write certain languages. (PHB p.17)
From their first mention languages are set out as a racial benefit. Two exceptions arise--Druidic and Thieves' Cant--as class benefits. Later, we see that knowledge of a language may arise from a background (p.125) or from extensive training (p.187). Which gets us to my interpretation:
Languages are part of your deep background.
Language acquisition as a racial feature arises from assumptions about segregated communities; the DMG (pp.20-21) discusses ways in which one might adjust these assumptions and how that might impact language acquisition. (They give the example of a racially-blind kingdom-dependent language system as an alternative.)
Language acquisition as a class or background feature is more-explicitly based on long times spent in the relevant community/diverse settings/life of study. Note the acolyte and sage gain two languages; guild artisan, hermit, noble, outlander each gain one. Alternately, you can pay to train for 250 days and 250 GP. This also constitutes a large amount of time, effort, and investment on the part of the character.
Thus, changing your ability scores, statistics, or skills have no effect on your languages. Because those changes haven't changed your experience, by which you acquired language. (Admittedly, those changes might impact your ability to hear, speak, read and/or write, however.)
Languages aren't a skill. They aren't tied to an ability modifier and your broficiency bonus in that way because they're binary: you can't (RAW) be more- or less-skilled in a language.
Languages aren't pegged to attributes. But they used to be. Originally PCs were guaranteed two languages: common and alignment. INT>10 made it possible to know more languages. In 1e your intelligence capped the number of languages beyond your base (racial/class) languages that you could know. In 2e your intelligence capped the total number of languages that you could know, all the way down to INT=1 capping you at zero languages: "while unable to speak a language, the character can still communicate by grunts and gestures." (PHB1e p.10, PHB2e p.16)
[ed.: I'm working off of retroclone material for the Original cite: if anyone's got a good cite to edit in I'd appreciate it.]
Is it related to personality? Personality isn't really a defined term in D&D, so this gets sticky, fast. For our intents I think it's easy enough to say "no," but recognize that language and personality formation are interwoven in real life in a way our game just isn't trying to simulate.
I have always read
You gain the selected language as a bonus language,
as meaning that you add the language to your list of known languages when you create your character (as a bonus language), not that you add the language to the list of bonus languages you can choose from to learn with a high intelligence modifier. The reason I believe this is that it says you "gain the language as a bonus language," not "add it to your available bonus language options" as other similar features do.
This is no different in my view from gaining a bonus language from a high intelligence modifier.
You apply your character's Intelligence modifier to:
- The number of bonus languages your character knows at the start of the game.
I interpret this as meaning that it is a bonus language because it is not a language you have learned through a rank in linguistics or from your racial features -- that is, it is a bonus on top of your standard known languages. Essentially, you have a list of languages to choose from, and when you gain one from high intelligence or a class features, it becomes a bonus language. They are bonus languages because they do not require ranks in linguistics to learn them (because a linguistics rank allows you to learn any language). When you become an oracle you gain that language as a bonus.
The text that follows,
At 5th level, pick an additional language to speak in combat and
add it to your list of known languages,
indicates to me that the language added at 5th level is in addition to the bonus language gained at level 1.
Unfortunately, there is no real explanation for why the game writers used two completely different phrasings to mean the same thing, if you accept the premise in this answer as true, and, absent any developer or writer commentary on why such choices were made, I doubt we can make a determination on that.
Best Answer
Rules-as-written, yes.
Is language part of the creature's "statistics"? Yes. Monster Manual p.6 describes "statistics" thus:
That heading is followed by sub-headings for Size, Type, Alignment, Armor Class, Hit Points, Speed, Ability Scores, Saving Throws, Skills, Vulnerabilities, Resistances and Immunities, Senses, Languages, Challenge, Special Traits, Actions, Reactions, Limited Usage, and Equipment. So yes, language is specifically part of its statistics, and, rules-as-written, you gain it when you shapechange.
Of course, the DM is free to rule otherwise, and many DMs will rule that you don't gain languages since it doesn't make a lot of sense. But the question does ask what the rules-as-written answer, and technically, you gain langauges.
You also retain your existing languages:
As a side-note, nowhere in the rules specifically refers to a language as a proficiency. For example, on p.14: