Honest question, what about another equipment slot? Logis still have an advantage due to fitting bonus and cloaky scouts need one for the cloak.

yes

Once Scout got 2 why move from that suit to assault (in current state)? It was the same problem when logi assault was a thing - people used this suits for the added equip slots. By giving Assault there is less of a reason for people to be dragged to the other suits. e.g. With Logis having four equip slots those who want to logi will

More HP and PG/CPU are reasonable.

Equipment is a no no. Yes you can argue that a repping nanohive makes you a better slayer, but only for point defense which should not be a trait of the Assault. Assaults need to be extremely mobile killing machines, not something that encourages people to camp / be psudo Sentinels or Logistics.

I strongly advise you to NOT change the rate of fire. Rate of fire is a tool used to control minimum range in weapons, specifically the mentality that lower fire rate is poor for close range (Rail Rifle) where high fire rate is quite good for close range (Assault Rifle). While ROF increases DPS, it also modifies that minimum range. The issue with this is that shorter ranged weapons such as the Assault Rifle will gain close to no benefit from a decrease in minimum range, whereas a Rail Rifle would gain a huge benefit. This causes certain weapons of the same class to benefit from the bonus far better than others. If you want to up DPS, increase the damage per shot, not the fire rate.

Medium Suits as a whole should be focused around powerful HP regeneration. They should have the shortest downtime between engagements and I firmly believe both Assaults and Logistics should share in these defensive capabilities (Logistics to a lesser extent)

Racial Weapon Support skills are great. Yes Commando and Assault are redundant, we can't remove commandos, but don't be afraid to make them similar. Good reload speed makes to Commando proficient with light AV weapons which typically have small magazines, whereas Assaults should get support skills for Anti-Infantry weapons. The magazine size/suppression concept for Commandos is also one worth looking at (just be prepared for Shield HAV pilots calling for nerfs when a Commando runs up with 2 Plasma Cannons that can each fire twice without reloading), but I would still feel comfortable if both Commandos and Assaults received the DPS bonus.

Grenades bonuses are great idea for Assaults.

I'm thinking give them the 2% damage per level that commandos have, and give commandos 20% increased magazine size and max ammo. Then give each assault one bonus for their racial rifle, and one bonus for their racial tank.

That being said the idea of an increased magazine/ammo capacity for Commandos is growing on me.

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The biggest issue with this however comes down to the Amarr. Since the duration that Amarr weapons can fire is directly linked to heat buildup, the Amarr Commando would gain little from a bigger magazine, as it would need to stop shooting in order to let the weapon cool down first before continuing to fire. The only reasonable way to really counter this is to give them heat reduction, but since that's going to the Assault...it's a messy problem. You could consider shortened seize delay and reduced feedback damage, which could get interesting.