Re clearer photos:
Consider a 1" sensor camera (or larger than 1"). G7xII, G9xII, g5x, etc will all give clearer photos due to the larger sensor, all else being equal (technique, etc.). This is especially true in low light. Of course an apsc-c or full frame DSLR will also give clearer photos but I assume you are looking at a point and shoot type camera. Most of these 1" cameras are going to have much less reach though than the sx730/sx740.
In regards to image stabilization while moving:
As your reach gets longer image stabilization becomes much more important to counter the movement of the camera (camera shake). With DSLRs if you were shooting at 960mm equivalent many poeple would try to have really really good stabilization (think $600 tripod plus $600-$800 gimbal mount on top of tripod).
sx730 has incredibly good image stabilization, well beyond anything I've used with DSLRs. But when you are moving at long reach it is an almost impossible task without very high end stabilization equipment. So when taking stills at long focal lengths, go for good technique of resting camera on something stable, tight grip, and gentle squeeze of shutter. And don't move the camera at all. If you are talking about taking video while walking etc. at lower focal lengths, that is primarily a technique thing also. No matter what camera u use taking video while moving the more you act like a robot and keep camera very stable the better the video will be.
Bottom line:
I own sx730, g9xII, g7xII, full frame DSLR and have owned, panasonic, sony point and shoots as well as Nikon and Canon APS-C DSLRs. IMO the sx730/sx740's role is best as a long range camera that fits in your pocket. I can take pictures of Jupiter and Saturn even with it which My DSLR with expensive long lenses cannot. Sx730/sx740 is not the best for an all around do everything camera. I use my sx730 paired with g7xII for travel, G7xII gives exellent image quality including good low light (for a point and shoot) but has limited reach. SX730 has crazy long reach, incredibly good image stabilization, and punches well above it's weight for wildlife and long range but has somewhat less image quality compared to larger sensor cameras, especially in low light. Both g7xII and sx730 are the same external size (small). So my recommendation is keep your SX730 and use it for it's best role (long reach that fits in your pocket). Then add a 1" or larger sensor camera to do landscape, portrait etc. One example is u can buy a g7xII refurb for $429-$479 on sale on Canon's website (some have found new, non refurbs for close to these prices also). That way your 1" sensor camera is the "all around camera" and your existing sx730 is a special purpose (long reach) camera.