Since you have both TCS and TPMS warning lights lit, your problem shouldn’t be related only to TPMS system, and IMO that’s why you can’t just do TPMS reset. If you live in snow belt area, my guess is your problem is from those ABS speed sensors. One of more of these sensors may be corroded and malfunction. Check the condition of these sensors and clean up the area including the toothed ring and ABS sensor with the wheel off. You may have a hard time to remove the rusted ABS sensor, and Mazda doesn’t offer any dedicated info of which ABS sensor malfunctioning like some other car brands (VW?), so you may have to swap them out one by one with a new sensor if you can’t find any obvious physical damages.