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ROS Noetic targets Ubuntu Focal which comes with Eigen 3.3.7
As you need Eigen 3.4.9 I would expect that to only add API elements and not have significant backwards breaking changes to the relatively simple elements of eigen that tf2 and eigen conversions takes advantage of. 3.4.0 is the default as of jammy
To that end you should be able to install and use Eigen 3.4.9. There may be some minor tweaks that are needed to the code base, but as long as it stays in the 3 major version I would expect it to be generally compatible, but obviously it's not tested or supported so you'll be on your own to make it work.
Note: When you upgrade the version of Eigen any package that is building against it will need to be built from source on your system so that everything that you're using will be using a consistent version of Eigen. You should not use the binaries of anything that uses Eigen if you're upgrading it.
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