What resolution are you playing at? Targeted frames? What settings in games are you playing at? What types of games? Cpus age waay better than gpus in the context of frames and gaming.Upgrading your cpu might net you a 10-15% performance boost. But it sounds like you’re playing on a high fps limit, low res machine. I would recommend increasing your resolution or getting a new monitor first. Resolution has minimal impact on cpu and more of an impact on the gpu.
ON 1920X1080 the cpu is generally more of a bottleneck than the CPU. For instance i have a 2070 Super and a 3600x in one machine and the gpu will see higher performance gains than the Cpu at that resolution. Even though the Cpu would be considered weak by calculators in practice the Gpu gives bigger gains.