Strangely I was in your situation few weeks ago about same bulid then finally settled for 13600k and rtx 3070 that what was in my budget at the time and gave my gtx 970 to my bro and build him new PC with 13500 and ddr5 6000 MHz and what's really funny now they released 14 gen after I built both PC and now the prices are dropping and I bought the 13600k for 410 USD and 13500 for 245usd and used rtx 3070 for 329 usd
Strangely I was in your situation few weeks ago about same bulid then finally settled for 13600k and rtx 3070 that what was in my budget at the time and gave my gtx 970 to my bro and build him new PC with 13500 and ddr5 6000 MHz and what's really funny now they released 14 gen after I built both PC and now the prices are dropping and I bought the 13600k for 410 USD and 13500 for 245usd and used rtx 3070 for 329 usd