Bards:
Using Bardic Inspiration is now a thing you do as a Reaction to somebody failing a D20 Test, as opposed to giving it as a Bonus action and hoping it's useful in the next ten minutes. This is a big upgrade, and I approve.
You can also expend Bardic Inspiration as a Reaction to HEAL people after they take damage. This might be OP tbh.
On the other hand, you have far fewer uses of Bardic Inspiration. It's now Proficiency Bonus times per Long Rest. That does balance it.
You don't get the Font of Inspiration ability until 7th level (used to be 5th). That's the ability that lets you recover Bardic Inspiration on a Short Rest instead of a Long one.
Bard spell list is considerably curtailed. They can only use Arcane magic, and only from the Divination, Enchantment, Illusion, or Transmutation schools.
However, they can now change up their prepared spells on a Long Rest from the entire Bard spell list, a la Clerics, Druids, Artificers, and Paladins.
So at Level 2 Bards get a thing called "Songs of Restoration". This adds a suite of 5 bonus spells to spells known (one at 2nd, 4th, 6th, 8th, and 10th levels). These include healing word, lesser restoration, and mass healing word.
Lore Bard is mostly unchanged but one HUGE change is that Additional Magic Secrets at 6th level is gone, replaced by Cunning Inspiration, which basically makes all your Bardic Inspiration dice roll with advantage. That is a way worse ability than Additional Magical Secrets.
Of note: cantrips (sometimes referred to a 0-level spells in this doc) can be switched out on Long Rests just like levelled spells.
Jumping down to the spell lists. One thing that immediately jumps out at me is that the Booming Blade and Green Flame Blade cantrips don't seem to exist.
Hex is accessible to Bards.
They also pick up a several good spells they didn't have before by virtue of having access to the Transmutation school, including Fly and Haste.
They lose Dimension Door though.
All in all I think this is a solid Bard. Power-wise it has some plusses and minuses over the current Bard. I don't think the Bard NEEDS this overhaul, but neither do I think it's a war crime. I do think the Lore Bard losing Magical Secrets is likely to cause some gnashing of teeth in the community, as that is a much beloved ability for them.