Basically, my requirement is to shoot some birds and flowers

For flowers, you benefit from a macro lens. Not very expensive. Even a basic DSLR / mirrorless camera works. Even a point/shoot camera could be enough. Image stabilization can be beneficial for macro shots because to make depth of field less thin, a small aperture is required which requires long shutter speeds. For macro image stabilization, such systems that compensate for camera shift in addition to camera rotation are preferable.

For birds, the requirements are stricter. You require:

• Camera that is comfortable to be used for long periods of time, so that you can easily hold it in your hands steady
• A long telephoto focal length
• Ability to set very fast shutter speed (1/1000 s - 1/2000 s)
• Big enough aperture opening and big enough sensor that you can obtain enough light to have a non-noisy image in typical shooting conditions. Later generation sensors are better than older generation sensors in avoiding appearance of noise.
• A camera+lens system that has very fast autofocus with focus limiter and option to avoid hunting for focus when focus cannot be found
• Some means to find focus when the bird can be anywhere on the frame. Mirrorless caneras can have object detection to select the focus location, good DSLRs allow selecting multiple focus points so that aiming the camera precisely is no longer necessary.
• Burst shooting with good frames per second figure on the camera body, with servo autofocus

Note image stabilization is not in this list for bird shooting requirements. The reason is simple: you probably want to use so fast shutter speed anyway that image stabilization would be of marginal importance. When shooting birds in low light, image stabilization could benefit you because you might want to use a slower shutter speed then because of necessity.

No way could you achieve all of the bird photography requirements with a point and shoot camera. You really benefit a lot from an interchangeable lens camera.

For birds, get a telephoto zoom / prime lens on an interchangeable lens camera. Some good choices for Canon:

• Canon EF-S 55-250mm f/4-5.6 ($250 new)
• Canon EF 400mm f/5.6 ($1500 new)
• Tamron EF 100-400mm f/4.5-6.3 ($800 new)

For Nikon, the Tamron 100-400 is available and I recommend it. Nikon 300mm f/4 + teleconverter could be another prime lens option. The closest lens to 55-250mm in the Nikon world is 70-300mm.

For Sony, lenses are expensive and the Tamron 100-400 is not available. Sony 100-400 is available, and 200-600 could be another option. There is no cheap 400mm prime for Sony. The Sony 70-350mm lens could offer lots of focal length for crop sensor cameras.

Full frame lenses are better than crop lenses, delivering far superior image quality. For serious shooting, I recommend the full frame lenses over crop lenses. Example:

Canon EF-S 55-250mm on crop sensor:

Canon EF 400mm on full frame:

Yet, with EF-S 55-250mm you can get adequate shots. The lack of focus limiter annoys me:

The reason why I got such a good shot with the poor EF-S 55-250mm lens was that I saw a bird on a fence. I took a picture (requiring some time to obtain autofocus), took a step closer, took another picture, took a step closer, etc. until I was so close the bird started to fly. Then I took a picture of the flying bird. The autofocus was already very close to being in focus due to using it repeatedly while stepping closer. So, I was able to have a picture of a flying bird.

I would say that for someone who regularly takes pictures of flying birds, a focus limiter is a must. It is available in Canon EF 400mm and Tamron EF 100-400mm but not in Canon EF-S 55-250mm.

The 35mm equivalent focal length 400mm is in my opinion a bit short. But, longer focal lengths may get you into more expensive + more heavyweight lens territory. You could consider adding a 1.4x teleconverter if using 400mm on full frame, or shooting 400mm on crop sensor so you don't need a teleconverter.

Then, what camera to get? My recommendation would be a ~$1000 high end crop sensor camera. The crop sensor is better for bird shooting because it has a "built-in 1.6x teleconverter". It's hard to recommend a Canon mirrorless camera for birds in flight right now, because the RF cameras have poor frames per second and a slideshow-like viewfinder when shooting in burst. Sony could be better, but then again I know nothing about Sony lenses + cameras other than the fact that Sony has better fps.

Oh, and also this advice is for shooting birds on a budget in bright conditions. Near sunrise or sunset, the conditions are not bright and you'll probably need a ~$10,000 lens plus the muscles to haul it around.