How do I check the condition of the battery on a 13" MacBook Air (mid2012)

One way to check easily: see https://support.apple.com/guide/mac-help/check-the-condition-of-your-computers-battery-mh20865/mac

For more details:

In the Menu Bar, click on the Apple logo

Then About This Mac

Then System Report

Under the Hardware heading will be a sub-heading called Power. Click on that.

That will bring up Battery info.

Have a look at the Health Information section

Displayed will be Cycle Count (see https://support.apple.com/en-us/HT201585)

Condition (current condition of the battery)

Maximum Capacity. Capacity will start off at 100% when the battery is new. Capacity will drop down as the battery is used and ages

See https://www.apple.com/batteries/ for more info