MacBook Air M5 Battery Health Dropped to 94% in 6 Months with 111 Cycles — Is This Normal?

Is this normal, ...

Yes. It's normal. 94% is fine. Nothing wrong.

... or should I contact Apple Support for a battery check under warranty?

It's up to you but they will tell you what I just did.

Apple does not have to check anything. You already did, and it's normal. Contacting Apple will just be a waste of your own time. If it diminishes to below 80% then they will be interested.

In or out of warranty, Apple will refuse to replace it even if you offered to pay for it yourself.

Can battery health increase again to 96% or 100%?

The value is algorithmically determined. The algorithm is not publicly available, and it has been known to change from one macOS release to another, or one Mac model to another. It can increase or decrease a percent or two from one charge cycle to another, but batteries start life at 100% and will never again return to that value.

As John Galt told you, it is normal and Apple will not be willing to do anything for your battery because they consider the battery "good" until it reaches 80% capacity or has gone through 1000 cycles, whichever comes first.

Mac laptop batteries sometimes decrease in capacity faster at first and then stop decreasing. It is not linear. For instance, my 2019 Macbook Pro was at 85% about 16 months ago. Now it is at 86%. I have also seen fluctuations over ~ days to weeks of +/- 4%, so that is the level of "noise" in the measurement of "battery capacity."

Just be sure to connect the laptop to a charger whenever one is available and make sure battery health management is active. I would leave those settings to the Apple defaults.

P.S. Your other question: yes, you will likely see the battery capacity level go up now and then. Mine has "increased" by about 2% several times over short timespans (a few weeks) more than once. And my Mac is 7 years old (original battery). Your is 6 months old, that just is too short a time to draw any conclusions. I looked back at my battery utility log records and it shows mine dropping to 94% after 7 months with a total of 12 cycles (was on the charger most of the time). But it slowed way down after that in terms of how fast the battery capacity dropped.