Thyme runs and spreads pretty well among grass in my experience, and bee balms (Monarda spp) can do pretty well too for something taller, but they’re so pretty I wouldn’t mow them. Other good low-growers include things like wild strawberry and heal-all (Prunella vulgaris).
Autumn is also a great time to plant dormant and bare root plants to let them root over winter and early spring, for any patches you’re looking to fully transition into multi-year plants.
Tysm!