I agree with the above assessment that upgrading the 9 year old system is less preferable than the Ryzen + AM4 platform, from a cost per performance standpoint.
Nonetheless, if you wish to proceed, then the concerns will be availability, compatibility, and power draw.
Many mid-range Phenom II X4 are readily available, such as the 945 you found. There is always demand for the fastest parts to "max out" older platforms, but since supply is limited to parts already manufactured, pricing goes steadily higher - often way past a reasonable amount for the performance.
In my experience, HP is usually pretty good about CPU compatibility, IF the BIOS is up to date. It is likely that all of the Phenom II X4 CPUs would be compatible with the latest BIOS. The other main concern is whether the motherboard hardware can deliver sufficient current for the fastest CPUs, which leads to -
The power draw of the Phenom II X4 910 included in the original computer has a TDP of 95W. Thus, any of the Phenom II X4 with TDP of 95W should be no problem, including HDX945WFK4DGM, HDX955WFK4DGM, and HDX960WFK4DGM. There are faster CPUs which have 125W TDP. These would also work if HP's motherboard can deliver enough current: HDX955FBK4DGI HDX955FBK4DGM HDX965FBK4DGM HDZ940XCJ4DGI HDZ955FBK4DGI HDZ955FBK4DGM HDZ965FBK4DGM HDZ970FBK4DGM HDZ970FBK4DGR HDZ975FBK4DGM HDZ980FBK4DGM. There is also one CPU that has a 140W TDP: HDZ965FBK4DGI Watch out for that one, as many of the AM3 motherboards at the time were not designed to reliably deliver 140W.
