Is there a janky way I can more securely attach charger to its port for my old 2012 MacBook Air?

It works fine if the charger is plugged in, however, since it is attached magnetically, it gets disconnected very easily.

The MagSafe power adapter is designed to be easily disconnected, but the force required to do that is greater than the USB-C ports that superseded it.

Perhaps it needs to be cleaned: Apple Portables: Troubleshooting MagSafe adapters - Apple Support

Refer to Step 8. Routine inspection and cleaning is required.

If you are going to use tape, then make sure to use electrical tape as any other kind of tape may be a fire hazard.

Personally I don't recommend this in case you need to quickly pull the cable from the laptop in an emergency.

Definitely do NOT use glue!

Keep in mind if the battery actually has an internal fault it can cause performance issues and maybe even a safety issue with the laptop. Check to make sure the battery condition is not showing "Service Battery". Option-click or Right-click on the battery icon on the menu bar to see the battery condition.