But these police don't work for the state government. They worked for the Adams County government. The immunity waiver you linked explicitly only applies to the state government.
> (A)(1) The state hereby waives its immunity from liability,
and then "state" is defined in https://codes.ohio.gov/ohio-revised-code/section-2743.01
> (A) "State" means the state of Ohio, including, but not limited to, the general assembly, the supreme court, the offices of all elected state officers, and all departments, boards, offices, commissions, agencies, institutions, and other instrumentalities of the state. "State" does not include political subdivisions.
> (B) "Political subdivisions" means municipal corporations, townships, counties, school districts, and all other bodies corporate and politic responsible for governmental activities only in geographic areas smaller than that of the state to which the sovereign immunity of the state attaches.
Additionally even if the officers did work for the state, the immunity waiver still would not apply to the action of breaking down a door while executing a search warrant.
> (3)(a) Except as provided in division (A)(3)(b) of this section, the state is immune from liability in any civil action or proceeding involving the performance or nonperformance of a public duty
and Ohio state law specifically authorizes breaking down doors to execute search warrants so this action would be one "involving the performance or nonperformance of a public duty"
> (A) When making an arrest or executing an arrest warrant or summons in lieu of an arrest warrant, or when executing a search warrant, the peace officer, law enforcement officer, or other authorized individual making the arrest or executing the warrant or summons may break down an outer or inner door or window of a dwelling house or other building
https://codes.ohio.gov/ohio-revised-code/section-2935.12