Digesting food takes a lot of energy. Your body literally changes where blood is flowing after you eat to send more to your digestive system. That means there is less blood for other things like your muscles.

Your body tells you to slow down.

Wow that's actually insane. I have never thought about this. Thank you!

It's called postprandial somnolence, and it's not perfectly understood, partly because there's a lot of stuff potentially going on. We know there's a big shift with eating from the "fight or flight" sympathetic nervous system to the "rest and digest" parasympathetic nervous system, and this shift means overall low energy and a drive to reduce muscle use and send blood to the gut instead. There are probably a bunch of other shifts in the brain that contribute, though. Interestingly, chemicals like histamine and orexin that regulate appetite also strongly regulate sleep (i.e. blocking histamine makes you sleepy and hungry.)

Digestion requires huge energy.

It is diverted away from all other bodily systems, making us feel sleepy.

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why is this happening only after a certain age?

This is also why intense workouts and adrenaline situations cause stomach distress.

Shunting blood away from less immediate things like the stomach and keeping it available for muscles is a survival mechanism. It doesn’t matter if your meal is properly digested if you’re dead in the next few minutes to whatever the threat is.

You mean brain gets less blood (oxygen)?

Research is a little mixed, but it looks like the brain specifically doesn't get less oxygen during digestion. Your brain does coordinate signals telling you to slow down though.

I have read that we feel sleepy when our brain doesn't get oxygen.

That's not the only reason we feel sleepy though.