Both EF 300mm f2.8 L and L IS, not fully compatible
Neither the original 300/2.8 L or the 300/2.8 L IS have been supported by Canon for the very highest fps shooting on RF bodies. Generally only IS II and later Canon lenses are given full compatibility with the RF series.
From what I have gathered they get the second tier fps which is 12 to 20 fps, depending on the camera. They do not get the top tier 30 and 40 fps settings.
Mechanical fps also drops to the tier 2 level of approximately 5, 6.7 to 8 fps, again depending on the body.
I have the 300/2.8 L released in 1987 and the 500/4.5 L released in 1992. Those five years provided noticeably better AF on the 500/4.5. I use them on a 5DSR so AF should be somewhat better on RF bodies. I have found the 500 autofocuses the same with and without the 1.4x III. The 300 is still extremely good, but I do notice that in poor conditions it will hunt more often than the 500. The 500 rarely hunts at all. I use the 300 with the 1.4x on a very regular basis and it does extremely well. In the most challenging situations the 1.4x does lower the AF capability. The EF 2x II is virtually unusable with AF. Perhaps RF will improve this. The IQ is still very good.
Obviously the 300 and 500 are very different lenses but they weigh about the same and I managed to buy mine for about the same amount. If you anticipate using the 300 with either teleconverter a lot, the 500 is definitely the superior lens. The 500 with 1.4x III has amazing image quality!