I've used a lot of PowerShot cameras over the years, from the small-sensor models through the 1-inch models. Of course, models like the G7X MkII with its 1-inch sensor produce excellent image quality but these are outside of the budget you laid out. I had great success with a few of the small-sensor models, the Elph 330 HS (this became a bit of a cult favorite), the SX280 HS (25-500mm lens), and the SX50 HS (24-1200mm lens). The little Elph has a very sharp lens and for whatever reason, Canon chose this particular model to emphasize image quality by putting high quality lens elements in it. It's completely automatic and doesn't allow a lot of control, but it produces outstanding results. The SX280 HS also has a very sharp lens with a great focal range, and it allows you full control over your settings. It's also surprisingly good at tracking subjects. The SX50 HS is a wonderful camera although its age shows a little in the slower speed of operation. It also feels pretty plasticky. Having said that though, it also produces excellent images with excellent sharpness. I took one of these on an Alaskan cruise 6 years ago instead of lugging heavy gear, and I'm glad that I did. I got wonderful scenic shots and shots of distant animals that I wouldn't have gotten with my 7D/5D2 rigs. It also does a nice job of tracking subjects too. All three of these are older cameras from around 2012 but they still perform beautifully and are a lot of fun to use. Plus, they're also well within your budget. Check them out and see what you think.
Andy