The Apache License 2.0 is compatible with the GPLv3 and AGPLv3 but not the GPLv2: https://www.gnu.org/licenses/license-list.html#apache2. Using an AGPLv3-licensed library in an Apache 2.0-licensed program is allowed, but you must follow the AGPLv3 when conveying it, which is incompatible with the Apple app store ToS.
The combination of an Apache-licensed program and AGPLv3-licensed library is covered by both licenses, meaning that both need to be followed. This does not change the license of the program itself - the library could be replaced. Somebody could take away the users’ freedoms, but they would need to replace the library.