Under perfect conditions you can get big prints from a small compact but everything needs to line up - no cropping, perfect exposure etc. Noise comes in very quickly beyond base ISO or if you brighten the image in post. 12MP allows printing 26 x 20 at 150 dpi without re-sampling which is perfectly achievable with a good file 300 DPI will be better but not a huge amount. Switching to a different small sensor compact (not that many around these days) won't help a whole lot. To make a difference you need a physically bigger sensor. The biggest issue with the TG-6 is lack of manual controls you get two apertures f2 & f2.8 at the wide end plus f8 with an ND filter. It works great for macro stuff though without having to buy accessories.
Your next step up is the 1" sensor compacts - RX-100, G7-XII and LX-10/15 - image quality is better you get manual control (but not manual flash on camera) but you need a wet lens to achieve the same magnification as the TG-6. All options (incl TG6) need a wet lens to get truly wide.