Honestly, I'm not very familiar with how scientists determine Ro, but I think some models used to calculate Ro do take immunity into account.

This paper, for example, reviewed several studies and estimated that Omicron BA.1's Ro is close to 10. And an article from Guardian extrapolated the Ro to 13.3 for BA.2 and 18.6 for BA.5 based on epidemiological reports. But since such extrapolations are not backed by complex math, you have a point in that the BA.5's Ro estimate may be off.

https://www.theguardian.com/world/2022/jul/05/new-covid-variants-ba4-ba5-most-contagious-australia-third-omicron-wave-coronavirus-subvariants-ba-4-5