no plug icon fully charged

That is normal.

Battery Management.

How battery health management helps

The battery health management feature in macOS 10.15.5 is designed to improve your battery's lifespan by reducing the rate at which it chemically ages. The feature does this by monitoring your battery's temperature history and its charging patterns.

Based on the measurements that it collects, battery health management may reduce your battery's maximum charge when in this mode. This happens as needed to ensure that your battery charges to a level that's optimized for your usage—reducing wear on the battery, and slowing its chemical aging. Battery health management also uses the measurements to calculate when your battery needs service.

https://support.apple.com/en-us/HT211094?cid=mc-ols-energy_saver-article_ht211094-macos_ui-04022020

Service Recommended is the alert a user needs to worry about.

https://support.apple.com/en-us/HT204054

If you have "Optimized battery charging" enabled in Battery preferences,

it should eventually switch to the plug with a status "On Hold", i.e. the

adapter is not charging the battery and the MaBook Air is running off

the power adapter.