If you wear medium armor, you add your Dexterity or Strength modifier (your choice), to a maximum of +2, to the base number from your armor type to determine your Armor Class.
Generally speaking, the only main issue is you've nerfed Barbarian Unarmoured Defence until Con gets up to 20 - most every Barbarian now is going to default to Medium Armour and Low Dex (they might add Dex back on for saves tho). Conan is no more. But generally speaking, meh, not too much of an issue.
As far as monsters go, of the 22 medium armor wearing statblocks in the MM, 15 of them are unchanged. Four of them gain +1 AC, two of them gain +2 AC, and one (the ogre) gains +3 AC. That seems to fall within reasonable tolerance--other than the ogre, and I could just say what they are wearing is mechanically studded leather. And importantly to me, the guard statblock--one of the most common statblocks in my games--remains unchanged.
With bounded accuracy, mucking about with AC is always an issue for monsters and balance. and if fully a third of potentially affected Monsters see a rise, that could be a problem. Doubly so if they are mainly low level grunts who need the armour boost. For example, A CR 2 Ogre has AC 11 for a reason. That cranks up to AC 14 and that's a significant boost with 59 HP. I mean realistically you could lob that at a 5-man Level 1 party....If average attack damage is, say, 1d8+3 and average attack bonus is +5, that means you're averaging (60%*7.5) 4.5 damage per turn instead of 5.625. That might not seem much, but that's 14 attack rolls vs 10. With buffs, healing, maybe someone knocked unconscious.......could be a couple of turns of combat.....
Basically, I'd increase CR of those monsters accordingly, or ignore the medium armour buff for them.
Appendix: The Problem with Medium Armor
The question as to whether or not Medium armour does it's job depends on who can use it, and who might multiclass/burn a feat to get it.
Straight off the bat you can narrow it down who has medium, but not Heavy: Barbarian, Ranger, Knowledge Cleric, Valour Bard, Druid. So who benefits from it existing, currently.
Barbarian doesn't really. With +3 in CON (likely) you're starting at 13 anyway so Unarmoured Defence coupled with resistances covers the unlikely event first few levels you find a breastplate. Plus you get to play Conan.
Ranger and Valour Bard probably benefits non-thematic builds. Traditionally, these classes lean towards Dex (light armour) over Str and are both melee (have a primary attack stat), but if you want a STR build with a non-sucky AC Medium armour is there for you.
Knowledge Cleric benefits traditional themes. Clerics are thematically STR melee, and tend towards casting anyway, so Medium is a cheap AC buff.
Druid is a caster, so a cheap AC buff is useful.
Of the Light Armour characters, realistically burning a feat or multiclassing only works for
really wonky Rogues, Monks and Bladelocks (i.e. people who've clearly taken the seriously subverted choice for character/thematic reasons). Bards and Blastlocks could get cheap AC hikes, but the cost of a feat is expensive. So probably multiclass dips of Druid/Cleric I'd expect. They'd then fall under Druids (medium armour casters)
OK, so currently out of STR Bards & Rangers, knowledge Clerics, and Druids (including medium armour casters), who gets
hurt by current Medium armour rules?
Druids & Clerics benefit - They are unlikely to hike to Dex over 15 because of an attack stat necessitating Light Armour, therefore you get better armour for free. Anyway, being full casters, you're hanging around out back anyway. This is good stuff and allows you to focus on other stats other than WIS. The alternative is Light Armour and being wedded to huge DEX, or accepting a terrible AC. All options are viable because of medium armour: Scale mail (basically locks minimum AC to 14/15....decent compared to other casters).
Therefore, the only people who lose out are non-traditional melee characters - STR bards and Rangers who want to drop DEX below 14. And I would ask the questions, is this a) a major problem, and b) warrant a rule change. In both cases, I would answer: Probably not.
Unless you plan on taking Dex above 16 as a second stat (to the detriment of other social stats or CON), then having Medium Armour in the majority of cases is better than not having it. Therefore it serves it's purpose for existing - as a gap blocker for certain classes. I can see how, if you are making the choice to pump DEX for combat optimal reasons, it might nark a bit. But if you're only concern is combat optimisation (oh I'm sorry - I meant "Progressing your character normally".......) are you really taking sub-optimal choices such as a melee STR Ranger anyway???