You appear to be seeking to maximize the amount of background blur. Factors that increase background blur are:

• Distance to subject (closer)
• Distance to background (farther)
• Focal length (longer)
• Aperture (larger opening; smaller F-number).

Sensor size in and of itself is not a factor. However, it influences focal length choice and working distances. Smaller sensors force the photographer to use shorter focal lengths at longer subject distances, which reduce background blur.

To compare the FOV and background blur of lenses for different sensor sizes, convert values to "full-frame equivalents" by multiplying both the focal length and aperture by the crop factor. (This is equivalent to multiplying by crop-factor/crop-factor = 1.) For example, a 35/1.4 lens used on an APS-C camera will look like it was taken with a 52.5/2.1 lens on a full frame camera (35*1.5 / 1.4*1.5).

• The crop factor of your phone is about 5.64. That means photos taken at F0.95 will look like they were taken at F5.36 on a full-frame camera – assuming that parts of the image are not selectively blurred.

• The crop factor of the Sony RX100 is 2.7. A photo taken at F1.8 will look like it was taken at F4.86 on a full-frame camera. So, assuming "equivalent" focal lengths, the Sony camera would have slightly more background blur.

To compare the amount of blur produced by different lenses, calculate focal length/aperture. This gives the aperture size, which directly correlates with the amount of blur produced in resulting images. Higher numbers ⇒ more background blur.

This calculation can be applied regardless of sensor format because the crop factors cancel out. This can be used to determine the effects of different settings on zoom lenses.

• 10.4/1.8 = 5.8 (RX100 zoomed out)
• 37.1/4.9 = 7.6 (RX100 zoomed in)
• 18/3.5 = 5.1 (standard APS-C kit lens)
• 55/5.6 = 9.8

From these results, we can see that much more blur is produced by zooming in, despite the smaller aperture. The usual APS-C kit lens would produce more blur than the RX100. However, even "slow" primes can produce much more background blur than many variable aperture zooms.

• 35/2.8 = 12.5
• 50/2 = 25
• 135/2.8 = 48.2

Notes

• Exposure settings are still calculated with the non-adjusted aperture. The calculations noted above are for comparing how images will look.

• Some phones and apps have portrait modes that selectively blur parts of images. The above discussion excludes such effects. In principle, a depth map can be created and applied to any image, regardless of source.

• Narrow DOF is often confused with background blur and bokeh. It is possible to have narrow DOF with relatively little background blur.

• My personal experience with sensors smaller than APS-C has been disappointing. The difference among most compact camera sensor sizes usually has a greater effect on camera marketing than photographic results. However, there are compact(ish) cameras with APS-C and full-frame sensors that you could consider.

• If you are willing to consider interchangeable-lens cameras, I'd recommend considering a mirrorless camera. They typically have shorter flange focal distances, which allow greater flexibility in lens selection, if you are open to using manual-focus lenses. Even if you ultimately plan to purchase auto-focus lenses, manual lenses afford the opportunity to experiment with different lenses at relatively low cost.