Is it really so complicated/unusual to just say, as a PC you ARE susceptible to magics/effects that effect "Humanoids"?
File it under the heading of "PC members of their respective races are not the average/normal members of those societies."
Not really so difficult.
Everything else...sounds like everyone's basically on the same page.
Ability Bonus: +2 Str., +1 Wis.
Size: Large. You require a minimum space of 5' [wide] x 10' [long] to move in a straight line and make missile or pole arm...or go generic with "piercing damage" attacks. You require a minimum of 10' wide x 10' wide to turn and use slashing or bludgeoning weapons.
Equine Form: Your movement is 50' and your horse-body grants the following traits:
Beast of Burden: You carry up to double your Str. allowance without being encumbered. You can carry up to 3X your allowance encumbered (half movement).
Extended Reach: You add 5' reach to any/all melee weapon attacks.
Jumper: As long as you are unencumbered, as a reaction, you can make a standing horizontal jump of 5'. Given a minimum of 20' run-up, you can jump up to 15' horizontally or 5' vertical.
Charger: Given a minimum of 30' of run-up, successful melee weapon attacks deal double damage
Hoof/Kick Attack: You can use a bonus action to make an attack with either your front hooves or kick at a target at your rear/directly behind you. The target must be adjacent/reach 5'. Either attack deals d[whatever normal horse hooves deal] bludegoning damage and require a Str. save DC 10 + centaur's Str. mod. or be knocked prone.
Unwieldy: Due to general size, bulk, and weight of footstep, you have disadvantage to all Stealth rolls. You automatically fail any roll to climb any surface that does not allow for your equine feet/body, e.g. no rope- or tree-climbing, ladders, narrow (less than 5') ledges or beams, steep (more than around 50-60 degrees?) slopes, etc...
Honorary Humanoid: As a PC, you are susceptible to magics and effects that are stipulated for "humanoids" even though, as a species, you are not.
Keen Senses: You have proficiency with the Perception skill.
Centaur Weapon Training: While you use weapons as a Medium creature (single handed, versatile, two-handed), as normal, you receive the 2-handed damage of a versatile weapon when using it one-handed (there is no additional damage for using a versatile weapon two-handed). You have proficiency with
long bow, short bow, spear, and greatclub.
Languages: Common, Sylvan, Elvin