I would get a second opinion. Being a first generation Fiesta, your car probably has very high mileage. Many components could be worn past their reasonable lifespan. Including the CV joints in the drive axels. The steering rack and it's mounting bushings the ball joints in the control arms and even the bushings for said lower arms. My dad's 80 Fiesta required new upper strut mount bushings by year three. You really want to view that car as a senior citizen! Because it's old. Original parts that don't often need replacement may very well be tired out and potentially deadly! Just this week I replaced the lower control arms on my 2002 Focus hatchback. The ball joints were shot AND the arms were rusted to the point of being weakened and deadly dangerous.
It’s not a transmission slip. I thought it could have been something in the alignment, but the guy at the shop said that everything was good. He also mentioned that his dad had the same car and that the steering column (or something about the steering system) could be causing the problem. So we shall see!
Hello and welcome to the forum. Ford performance parts is still offering some suspension kits and such. The biggest improvements to the basic Fiesta are in the suspension and wheels. The front anti sway bar bushings are very soft. Polyeurathane replacements are available at any good auto parts store. Eibach company has rear axle beam stiffener bars that give you a close equivalent to the stiffness of the ST rear beam. A smooth induction tube and low restriction air filter element will have a noticable performance effect for not much money or effort. I have also found that using a high quality full synthetic oil, changed on a regular basis, goes a long way in preventing future issues with failing camshaft timing phasers. Just good basic maintenance and care will get you a reliable vehicle for many years.