Then your best bet is probably a PIR motion sensor mounted on the wall at about his shoulder height when he stands up.
Or an aqara mmwave sensor mounted on the ceiling pointed down at the bed (not the cheaper Sonoff or Tuya mmWave sensors, though).
Either would likely give you a quicker response than going through IFTTT, but you are also likely to get more false positives with the motion sensor than with the bed sensor.
With the aqara FP2 mmWave sensor you should be able to get very quick response and few false alarms but the integration with SmartThings still isn’t great. So it would work best either just with its own app or with Apple HomeKit or Home Assistant. (There’s also an Alexa integration, but that’s still cloudbased, so might not be quick enough for you.) that particular device isn’t Matter-compatible at the time of this posting.
PIR MOTION SENSOR
relatively inexpensive. Any decent Zigbee or matter over thread sensor should work with good response time
Lots of candidates available with good ST integration, including Aeotec Zigbee, aqara, and others. Don’t get a Tuya product for this.
When positioned correctly, you should be able to avoid the dogs
Works fine in the dark: it’s measuring body heat, not visible movement.
You may have to try some trial and error to get the position right. Remember that you get the quickest response tracking movement at 90 degrees across the sensor field, not straight on towards it.
Aeotec Zigbee:
https://www.amazon.com/Aeotec-SmartThings-Motion-Magnetic-mounting/dp/B095TZTGNB/
Third reality is a good budget brand
https://www.amazon.com/THIRDREALITY-Required-Friendly-Assistant-SmartThings/dp/B08RRRWK6B/
I do not recommend Z wave motion sensors for your use case, the Zigbee ones will almost always be faster.
AQARA FP2 MMWAVE SENSOR
More expensive than the competition, but also more accurate with more features which you will probably want for this use case.
Very quick response time.
Works fine in the dark and should have fewer false alerts than PIR sensors. Also, usually better and quicker at detecting absence of movement.
When used with its own app has lots of features that may be helpful, including the ability to divide into zones. For example, I have mine set up so that it will detect me in my bed but not my 75 pound dog in his crate.
However, there is no direct integration with SmartThings at this time, although both companies have said they are working on it. For now you could use the aqara app to turn on an aqara smart plug with a table lamp plugged into it, and then use a lux sensor connected to SmartThings to get an ST alert that way. That should all work locally. (or again use Apple home or home assistant.) hopefully we’ll get better integration in the future, but this method should work OK.
Aqara is working on the ability to optionally ignore pets, that feature hasn’t been released yet. If the dogs sleep on the bed, then again, it may take some trial and error to get the alert you want. If they don’t get on the bed often, then, having the sensor on the ceiling, pointed down at the bed might give you the most accurate results.
Only buy it from an approved distributor (including aqara direct at Amazon)— counterfeits can be a problem at some of the cheap online marketplaces.
https://www.amazon.com/dp/B0BXWZMQJ3
PRESSURE MATS
I personally would not recommend a pressure mat on the floor for your use case: it might present a tripping hazard, or your dad might end up getting on/off the bed without stepping on the mat. Also, it’s very common for dogs to want to sleep on the mat. I like them for situations where the person will intentionally use the mat, but not for this specific situation.
CONCLUSION
You may have to try a few things to see what works best for you. Just from your description, I’m probably most optimistic about a shoulder height PIR sensor, but you will have more feature options and even quicker response with the aqara fp2, so it might be worth trying. The biggest issue with that device is the lack of SmartThings integration at the time of this writing.