I am not qualified to speak on this in any way, but here my 2 cents:
I really like your relationship dynamic, and how you try to do everything 50/50. But keep in kind, this is not a contract. You don't have to do anything in particular so long as you're both happy.
What I'm getting at is that if your partner hasn't mentioned being dissatisfied, then by attempting to solve a non-issue you could potentially create one.
On the other hand, from your perspective, if you want to feel like you're doing more, then just do that. It doesnt have to be planned or signficant or anything at all really. It can be as simple as opening the door for them or taking out the trash or handwashing their car. Any time you have free time and want to help out more, just find something to do. If they've already done the housework, maybe that was their decision. Maybe they wanted to do that to make things easier on you. It's good to appreciate that, but it oeaves you with seemingly nothing to do in return. But housework isnt the only thing you can do to show appreciation. Give them a massage, get them a gift, secretely handle one of their responsibilities. Whatever you do, do not handle this as a bargain unless thats the relationship you two have. Ultimatums (this is my responsibility, that is yours, if you dont do yours i wont do mine) are always bad, and its not like youre doing this so they owe you. Presumably they feel the same way.