If a Path of the Giant barbarian is grappled, does that count as ‘not enough room to grow’

The DM will need to rule, and may well take narrative circumstances into account

There are several issues here:

• Does being grappled prevent the barbarian's size changing via Giant Stature
• Does the barbarian's size changing, via Giant Stature, break a grapple

Giant Stature and the grapple

There is no reason to believe that being grappled itself, regardless of other circumstances, is enough to stop growth via Giant Stature.

The Giant Stature feature of the Path of the Barbarian from Bigby Presents: Glory of the Giants says:

Giant Stature. Your reach increases by 5 feet, and if you are smaller than Large, you become Large, along with anything you are wearing. If there isn’t enough room for you to increase your size, your size doesn’t change.

That does not say how it interacts with grapple. And there is nothing about the grappled condition itself that answers the question one way or another.

The DM could simply rule that grappling always restricts Giant Stature or that grappling never restricts Giant Stature. Either one fails to take into account the many and very different circumstances in which a character can be grappled, and whether that grapple is somehow restrictive in such as way that the barbarian has no "room to grow".

A grapple can be as unrestrictive as holding another creature using one hand. The grappling rules say:

Using at least one free hand, you try to seize the target by making a grapple check

However, many monsters and spells grapple a target, through many varied methods: bites, tentacles, tendrils, weapons, adhesives, constriction, and other mechanisms. Not only are these grapples narratively different, a quick survey of monsters shows DCs ranging from 11 to 20.

So grapples from different sources are narratively different and should perhaps be treated as mechanically different.

Being grappled by the bite of a giant frog or the grasp of an irate innkeeper seems quite different than being grappled in the claws of an ancient dragon or the coils of a gargantuan snake. A DM may simply rule that the giant frog can't contain your growth and that an ancient dragon can, or the DM may want to impose some sort of contest.

Certainly, whether the character is somehow surrounded or contained is important, as is whether they are restrained.

How strong is the growth mechanism in Giant Stature? We don't know. On the one hand, it could be as feeble as can be imagined, and be stopped by even the constraint of a fist gripping cloth. Or it could be as strong as can be imagined, and be stopped only by something relatively unmovable, such as stone walls, which would restrict its room to grow. Something has to be strong enough to restrict it, otherwise, there would be no point in the "room to grow" limitation.

The rules don't say, so the DM needs to decide.

As a DM I would certainly lean into the narrative. If an irate innkeeper grabbed and grappled the fairy barbarian with a single hand, in no way would I let that restrict the barbarian's size change. Suddenly the innkeeper would have hold of a whole lot of enraged large fairy barbarian instead, and it would be interesting to see what happened next.

On the other hand, if the ancient red dragon, gargantuan in size and 30 strong, had the fairy barbarian in its claws, I'm not so sure. Perhaps that enclosing dragon fist is strong enough to stop the barbarian's growth, leaving "no room to grow". Either outcome is enjoyable. A possibility might be to allow the dice to decide.

Ending the grapple

Allowing the size change does not necessarily mean the grapple ends.

For instance, the ancient red dragon above probably doesn't care that you weren't large when the grapple started, but are now.

For small or smaller opponents, the size change likely ends the grapple.

You mention being grappled by a small or smaller opponent. The grappling rules do not say, but it is reasonable that a grapple can't be maintained if circumstances (such as a size change) would no longer allow it to be inititated. See "Can you maintain a grapple you are no longer capable of initiating?".

I say, "likely", because there could be other circumstances to be taken into account. A small grappler might be grappling by some mechanism (such as a spell?) that does not care about size.

For medium or larger opponents, the size change probably does not end the grapple.

The size change alone, however, might give the DM a reason to retry the grapple check. In the case of the frog or the innkeeper, just the surprise from a sudden change in size might be enough narratively to warrant a new check. In the case of the ancient red dragon, even if allowing the size change, the DM may well decide that the character is still grappled.

The size of the matter

A word about your size. Fairy PCs are size Small. According to the Height and Weight description of the Fairy race:

Player characters, regardless of race, typically fall into the same ranges of height and weight that humans have in our world.

and narratively adds:

Fairies are a wee folk, but not nearly as much so as their pixie and sprite friends

So merely from the description that you are playing a fairy PC, we do not know the actual size of your character, although probably roughly the size of a small human. At least narratively, that might make some difference, although perhaps not strictly by the rules.

However, in some of your other questions, you have mentioned that because of Reasons, your fairy barbarian is a bit over 3 millimeters tall.

Now, this is entirely homebrew territory, but it definitely changes the narrative. I already enjoyed the idea of the irate innkeeper grabbing the 4-foot-tall fairy barbarian that was trashing the place, "I'm showing you the mud outside, you little winged troublemaker", only to find out they had something else quite different in hand.

The image of the 3 (and a bit) millimeter fairy running amok on top of the bar, then the hand of the innkeeper descends, the innkeeper thinks hmm, tiny but really strong, succeeds on the grapple anyway, and then suddenly has hold of a large and enraged fairy barbarian is just too much fun.

How large? You didn't ask in your question, and the rules don't say, and since your diminutive stature is entirely homebrew, the answer needs to be also homebrew, but the feature says you're large, and your reach increases by 5 feet. No matter what, that's a lot of very angry fairy.

You gotta fight for your right to party

I mean, to grow.

I gotta disagree with this teacher DM you speak of. First of all, they're not THE DM, right?

In the end, only the actual DM's opinion matters (okay, perhaps the other players in the game). Everyone else can have an opinion, but it's just that.

So, who are you going to believe, some authority figure that you trust, or random strangers on the Internet? Right, random strangers on the Internet, for the win!

Seriously, I'm sure your teacher DM has good reasons for their opinion, but I'm not seeing any rules-basis for that opinion. So it's just that.

As a DM I grant great consideration to player characters and their features. Your character is a Path of the Giant barbarian:

Barbarians who walk the Path of the Giant draw strength from the same primal forces as giants. As they rage, these barbarians surge with elemental power and grow in size, taking on forms that evoke the glory of giants. Some barbarians look like oversized versions of themselves, perhaps with a hint of elemental energy flaring in their eyes and around their weapons. Others transform more dramatically, taking on the appearance of an actual giant or a form similar to an Elemental, wreathed in fire, frost, or lightning.

I think that needs to be respected. Furthermore:

Giant Stature. Your reach increases by 5 feet, and if you are smaller than Large, you become Large, along with anything you are wearing. If there isn’t enough room for you to increase your size, your size doesn’t change.

That should not be stopped by tissue.

Furthermore, the feature says "your reach increases by 5 feet" and "you become Large".

Me, I think you get these things. Exactly how, I'm not sure. Maybe you grow to 5 feet tall. Maybe 10 feet. Or maybe only 4 inches. But however big (or small) you are, in my book, you've got 5 more feet of reach and you control space like a large creature. Maybe you're physically large, maybe you're just really really angry and fast.

Because you are a HEROIC RAGING BADASS TEENY TINY FAIRY BARBARIAN with the heart and the glory and the magic and the myth of GIANTS! You make LOOK small, but you are BIG! Very very BIG! GIGANTIC! And you will NOT be stopped! You will NOT be contained! You will NOT be grappled! You will NOT be restrained! You will NOT be put in the corner! And anyone who tries, well, that's going to make you very, very angry, and bad things sometimes happen when you get angry! Grrrr!!!