New content has been delivered as new editions, supplements (optional), and errata (mandatory - for digital, at least). But 5.24 is being defined as something else like a supplemental errata. It's a bit of a paradox - it is both mandatory and optional. If a table is playing the 5.24 rules, those rules, including the class tables and class spell lists, become the default rules. 5e characters are converted unless they're not in 5.24. For the earlier example of the bladesinger with booming blade - they couldn't have booming blade RAW because Wizard is in 5.24 but, from a comment I saw, booming blade is not. Yet it is also fine to play a 5e character made with 5e rules at a table playing 5.24, so you can have a bladesinger with booming blade RAW. Both of these bladesingers can play in the same game. That's great flexibility, but forgive me, it's chaotic. I think that for practicality's sake 5e and 5.24 may work best if treated as different editions.
You are deeply misunderstanding the situation, if you think that a Wizard from 5.24 cannot use Booming Blade. They absolutely can. Booming Blade is still a legal spell to be used. It is simply that if you open the 2024 PHB and see a NEW version of Booming Blade, then you should use that version.
The thing with it being "mandatory but optional" I think is also just making this far more complicated than it needs to be. It is actually brutally simple.
If you sat down at a table using the 2014 rules run by a machine, and tried to play a 2024 Fighter, the machine would spit an error message. The machine has no reference in its database to "Weapon Mastery", so your ability to use this is nonsensical to the machine. However, if you sat down at a 2024 table and ran a completely by the book 2014 fighter... that machine would have no problems utilizing the 2014 fighter. Everything referenced in the 2014 fighter makes sense to the machine and it would run smoothly. This is literally the only point on the mixing of the rules that matters.
Do the designers WANT you to run the 2014 Fighter? No. They made a better version of the Fighter, they think you should use that. Do you want to play a Rune Knight which isn't in 2024? That's fine, just like Booming Blade, the Rune Knight slots in without any problems into the 2024 rules.
Do they WANT you to take the 2024 Fighter and use the 2014 GWM Feat? Nope, they want you to use the new feat. But you CAN
CHOOSE to ignore that advice. The game functions with either, they just want you using the new material when it is provided to you.
Naming is functional and communicates compatibility for characters between editions. A lot of what I'm seeing is a broad handwaving about balance to state there's compatibility. But I think players' perception of balance can be pretty important. I would want at least a heads up if I was going to be playing a 5e monk, paladin, fighter, ranger, what have you at a table with a similar 5.24 character, or vice versa. We can play across versions, but that doesn't mean we should.
5.24 is backwards compatible in the way that the Borg are compatible with anyone. Just convert. It's funny, by stating 5.24 is backwards compatible, it defines 5.24 as a different edition. Because you don't state that a supplement or errata is backwards compatible. The linguistic gymnastics to say the books are backwards compatible instead of the new edition is backwards compatible is impressive.
tl;dr I think the naming matters because it sets expectations and player perceptions of fair play are more important than how balanced the characters might be.
If you are sitting down at the table with someone playing a Verdant Soul Sorcerer, do you know what to expect? What if I told you it was from a supplement focused on plant-themed characters and not from the PHB? Does that help you figure out if you should be playing at that table with that character? Is it compatible if you are playing an Aberrant Mind Sorcerer?
What if I go further and you are playing with an Inventor from the Crafting Compendium, which is a fully 5e compatible book? Do you know, just from that, if the Inventor is more or less powerful than the Artificer?
The issue here is you are thinking that there must be a clear, bright line drawn because these 2024 versions of the classes might be stronger and therefore it should be a new edition. But if I'm sitting down with an Oath of the Coven Paladin, a Gunslinger Fighter, a Way of the Leaden Crown Monk, and an Order of the Ghostslayer Blood Hunter... should I declare that a new edition of the game? All of those subclasses are officially printed in official 5e compatible books and materials. What if I wanted to use them in a 2024 game, would that suddenly make them sixth edition materials?
You are making this a big deal, when the reality is, it isn't any different than sitting down with any other rules changes from any other source.