Im not sure Intel has any worthwhile CPU's unless you are getting them used.
Currently E cores are mostly trash, and not all that "efficient" and letting a P Core turbo up and get the task completed uses less overall power.
Secondly Intel is lying about its heat output, and power use. Everything from 10th gen up is a power hog if you dont limit the performance to well below "stock" settings.
https://www.techspot.com/review/2612-intel-core-i5-13500/
This is a good match up between an i5-13500 vs R5 7600, which is the most interesting IMO. The R5 7600 seems to be about $15 less expensive for just the CPU and uses 3/4ths the power which will be a greater savings over time vs Intel. The AMD Motherboards also still seem to trend a bit lower in cost than Intel.
So overall its a good question. If you can get a use 13500 or one under $150 then its probably worth it, but at retail prices the 7600 will cost less to buy, and less to own while being similar in performance.