Is there a known way to make this data available in the activity page? I have noticed the changes affecting me quite a lot so I would like to track it long term. Thanks.
It seems there is no original Garmin datafield available for "Air Pressure".
There are several IQ widgets available - for example:
https://apps.garmin.com/de-DE/apps/00678298-6672-4228-9c82-c9aa00e43df0
The only datafield for air pressure I know (which can be integrated to your datafields), is available in IQ datafield "HMs DIY":
https://apps.garmin.com/en-US/apps/b0346b71-bf01-4070-96d6-3de66dcc8233
There is a value type "Pressure" which shows air pressure in hPasc.
EDIT:
Now, reading your post another time - maybe my answer is not what you asked for.
I think it is not possible to record air pressure and show it in Garmin Connect after saving your activity.