Sorry the S23 is not getting Exynos at all, they are only using Qualcomm SD 8Gen 2 in all markets. There is no indication than Exynos 2300 will even be made, so I doubt they would just make it for Google.
Preliminary details about what could be the upcoming Pixel 8 and Pixel 8 Pro have surfaced. Codenamed Shiba and Husky, respectively, these next gen Google Pixel phones are said to be running Android 14 and will be powered by yet another Samsung-Google SoC collaboration codenamed Zuma, which is likely to become the Tensor G3 with the same Exynos 5300 5G modem as the Tensor G2.