Yes and no. There are plenty of situations covered by state law, not federal.
The high school and / or college transcripts for military personnel are not federal.
Military members have drivers' licenses issued by states.
Military members' personal vehicles are registered and insured by a state.
The off-base healthcare professionals for TRICARE are licensed at the state level, not federal.
Contract laws for military personnel in base housing apply at the state level. A military member living in base housing who fails to pay their bills such as car loans, internet, mobile phone, etc. are dealt with at the state they're in, not federal. (Yes they can face charges in the military for the same but the court that liens would be filed in state or county, not federal).
There are agreements between feds and the states, as well as feds and counties. Some National Guard units operate out of regionally owned airports. If activated, the Guard unit falls under active duty military but still has to adhere to state and regional restrictions.
Many military bases have noise level and flight path restrictions set by local government.
Military bases have to comply with state level environmental regulations. Bases in California in particular face restrictions that other bases don't.
There are plenty of other examples. Lloyd Austin may find himself twisting in a knot trying to stick to his statement.
Yes I know. And all of those rules are ultimately established by federal law at some point. What matters here is, the DoD saying it will continue to operate according to federal law is a statement that says nothing.