Connecting Solenoid (12v DC) with a battery source (12v 23A)
Typical A23-type batteries are rated for about 15mA max load. Their short circuit current could be about 500mA. Estimating from that, the battery has an internal resistance of roughly 24 ohms.
The solenoid is rated for 6.5W at 12V, or 540mA. That is about 22 ohms.
Connecting those, you get roughly 6V over the solenoid with roughly 260mA of current.
That battery has no chance of operating the solenoid. It is meant for light pulsed loads such as remote controls, or even lighter constant loads.