This is largely up to the DM to determine, but it's probably worth talking about the reason for that clause.
In general, sections like these are just meant to tell everyone involved what the options are: "you become large" or "you don't grow bigger". It implicitly tells the DM and player that you can't use this power to grow large and ...
As far as I can find there is no official ruling. As you have stated all the applicable rules, and the RAW are still ambiguous (no clear RAI), I would say with a fair amount of confidence that this is a individual DM rule decision on the interpretation of the phrase:
If you lack the room to become Large
Mechanically there is no end difference to becoming ...
The order does count.
As you reported, the description of Giant's Might says (emphasis mine):
If you are smaller than Large, you become Large, along with anything you are wearing.
If someone has already cast on you Enlarge/Reduce making you Large, if you try to use Giant's Might then the size requirement is not met, hence you remain simply Large.
There is ...
The class feature description has everything you need to know.
The feature description for Giant’s Might is complete - you don’t have to look elsewhere to learn its effects:
As a bonus action, you magically gain the following benefits, which last for 1 minute:
If you are smaller than Large, you become Large, along with anything you are wearing. If you lack ...
If possible, the creature grows and is squeezing. When it grows, its weapons grow accordingly.
Let's say a Medium creature is in a 5ft-wide tunnel, and is Enlarged. Then it is now Large and squeezing:
A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that'...
Consult the Size Categories Table in the Monster Manual (p. 6) or the Player's Handbook (p. 191).
The Monster Manual defines creature size as:
how much space a creature of a particular size controls in combat.
2.5 × 2.5 ft
5 × 5 ft
5 × 5 ft
10 × 10 ft
15 × 15 ft
20 × 20 ft or larger
A creature's ...
There's a little table in the Monster Manual, in the first chapter that explains how stats work. It also gives the space that monsters take up on the battlefield. It's on page 6 of the book.
The spaces are as follows:
Tiny: 2.5 by 2.5ft
Small: 5 by 5ft
Medium: 5 by 5ft
Large: 10 by 10ft
Huge: 15 by 15ft
Gargantuan: 20 by 20ft or larger.
In the case of ...
The rules are inflexible on this point. The broom at its most can only carry 400 pounds before falling out of the air. You might try to reduce your weight for enlarge person. Additional magic on the broom which changes the brooms size will not give it more carrying capacity. I dont even know of a spell that directly will increase the carrying capacity of ...
The creature expands into the space of the other creatures
A medium creature surrounded by 8 small/medium creatures will occupy its original space and the spaces of 3 of the surrounding creatures in one of the corners.
The rules state:
Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.
There is no prohibition on ...
Giant's Might cannot override Enlarge if you no longer meet the condition for Giant's Might.
Giant's Might states:
If you are smaller than Large, you become Large
If you use Giant's Might to become Large, then cast enlarge/reduce to become Huge, Giant's might does not force you back to Large because it says you become Large only if you are smaller than ...
Technically, order matters
Other answer showcase this well enough but say enlarge/reduce was applied first, then you are already Large and becoming Large again (using Giant's Might) simply does nothing. Whereas, as already demonstrated in your question and its other answers, doing things the other way around means you would first become Large and then be ...