The AMG8833 has an INT interrupt output that pulses when the image changes. You wouldn't need to add the tft display if you didn't want it. Just monitor INT pin
Let's assume you are modifying an existing alarm clock
Arduino includes a sound sensor, AMG8833, momentary switch and a relay controlling the speaker.
Sound sensor detects the alarm,
Start monitoring the thermal image pointed at bed,
Image goes from hot spot to cold (you got up and left the viewing area),
INT stops triggering,
Open relay, silencing alarm,
You return into viewing area (bed), creating a hot spot,
relay closes, alarm sounds
After 15 minutes, hold relay open
Manually reset for next morning by pressing button and turning off alarm.
Most of this applies if making your own clock except no need for sound detector or manual reset
I found them to have a wide, almost 360° detection angle, very sensitive, and detects through walls. You can add a resistor to decrease the range. My experience trying this was it went from detecting most motion in the house to not detecting anything a meter away.
It's worth a try. Your results may be better than mine.
Do you really mean that? Or do you mean when you actually get out of bed? The former seems very complex but the latter could be as simple as a carefully improvised switch under your mattress.
Then go ahead and experiment with a switch positioned under your mattress as I suggested. I'd start with a block of wood with a microswitch on its top. A two-person trial and error session will determine the correct height. Use a simple LED---series resistor---battery (or other supply) for the testing.
EDIT: Scrub that suggestion because on further thought I think it would prove unreliable. Even if you slept alone, just turning over could trigger the microswitch. Other false alarms are easily imagined.
So instead I'd recommend a motion sensor, carefully positioned to only detect your movement after leaving the bed.
I've successfully used these in several projects, such as triggering a camera when a local fox makes an overnight visit. This is the one I used: https://www.ebay.co.uk/itm/113735908004