Cannot find a new Intel CPU chip that meets the integrated graphics requirements

Newegg has many for that LGA1200 motherboard

https://www.newegg.com/p/pl?N=100007671%20601351801&cm_sp=filter-_-INFOCARD-_-Subcategory-_-343-_-Property_601351801-_-2

This is the one I have https://www.newegg.com/intel-core-i9-10900k-core-i9-10th-gen/p/N82E16819118122

Guess what? Your system's CPU is now effectively obsolete. Adobe no longer supports any hardware than's more than four years old at this point, and Intel had already discontinued mainstream support for all 4th-Gen Core CPUs like yours in 2018. In fact, de facto the "latest" driver from Intel itself for your CPU's integrated graphics is based entirely on one that dates all the way back to the first release of Windows 10 in August 2015! Since then, only critical security fixes have been released for the newer driver versions for that integrated GPU.

Worse, the last version of Premiere Pro that supported your integrated GPU, Premiere Pro CC 2018 (12.x), was made permanently unavailable via the Creative Cloud desktop app back in late 2019. Adobe's older version availability policy, which had been implemented in May 2019, now restricts availability to the current major version plus the major version that immediately precedes it. At  this moment version 15.0 (Premiere Pro 2021) is now the oldest version that can be officially downloaded and installed via the Creative Cloud app.

And this is all because the chip manufacturers have in recent years become dictatorial, if not completely authoritarian, in their relationship with software companies. Adobe must comply with the hardware makers' demands or risk losing certification from those same hardware companies.

As for the Asus PRIME Z590-P, you will have to buy a lower-end 6-core/12-thread CPU such as an i5-11600K. Its VRMs are a bit too underwhelming for the 8-core parts like the i7-11700K, with the VRMs running a bit too toasty for comfort.

And the Intel UHD Graphics 750 that's on the i5-11600K, although technically not on the supported GPU list for Premiere Pro 22.x, is actually based on the Intel Iris Xe graphics that is on the list. The Iris Xe graphics has been gimped in the UHD Graphics 7xx series so that Intel could squeeze in desktop-class (as opposed to mobile-class) CPU performance in the same die area. Likewise with the 10th-Gen i7-10700K, whose UHD Graphics 630 is a gimped version of the Iris Plus graphics that is also on the supported GPU list.

You are only going to be able to buy a CPU that is made for your motherboard... so what is your motherboard?

My motherboard is type LGA1200 and I have an Intel i9-10900k