I can’t using SketchUp 2022 for Mac OS 13.
I have already sent information to SketchUp Support and have a answer that not support on this version.
I want to know in the future. Can we using SketchUp 2022 with Mac Newer version OS.
I am not a Mac user, but several users have posted on the forum about success using SketchUp 2022 with MacOS Ventura. I don’t know how their setup differs from yours.
I am not superstitious, but past experience (AutoCad, Archicad) has made me wary of installing version 13 of anything 
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The “official” explanation about requirements and additional compatibility considerations of the current version of SketchUp can be read here:
SketchUp Hardware and Software Requirements | SketchUp Help
Anyway, I don’t think the SketchUp team knows about future OS changes that are out of their hands, so I don’t think your question is appropriate here…
Usually, the SketchUp program updates are following the OS what is on the market. 
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I don’t think we’ll see support until the 2023 version.
There are usually 2 big updates for SketchUp a year - New release at the start of the year and a point release mid year.
As Ventura came out after this mid year timeframe, I would expect compatibility with the next release, which is normally jan/feb
I have an error with Bugsplat when lunching SketchUp Pro 2022 on ventura
Which version of Windows 11 are you using?
Actually OS 13 is Ventura, the latest OS released by apple a few months ago, so the question is appropriate.
When will SketchUp support Mac OS 13?
OP will soon learn to wait a year after every OS release before updating your computer’s OS in order to maintain compatibility and support from SketchUp and other softwares.
not necessary a year, but yeah, if you use your computer for work, you should NEVER update the OS before checking that ALL your softwares are 100% compatible.
And if, for any reason, you choose to do so anyway, you should ALWAYS be prepared to rollback at any sign of trouble.
And this is not just Mac OS, before changing my win10 pc to a win11 one, I checked all my softwares.
In general, there are no reasons to jump onto the band wagon and update right away. Security fixes are included to former versions anyway, and no new tool / gizmo is worth the pain of dealing with glitches and bugs. Especially with the version XX.0 or 1. They’ll rack up a lot of tiny bugs that went through the net of testing