It should not be too difficult to set up your new Mac, especially because your files are on an external hard disk.
You can install CC apps on 2 machines, just download the CC app and log in with your current account.
Be careful with the application versions you install, if you want to go back later to your older machine (but. maybe I misunderstood that), if you install newer versions than are currently on your Imac, you may run into problems once you get back to your older machine with files saved in a newer version.
So before using the apps, make sure that they are the same versions by installing the older ones.
https://helpx.adobe.com/download-install/apps/download-install-apps/creative-cloud-apps/install-previous-versions-creative-cloud-apps.html?x-product=Helpx%2F1.0.0&x-product-location=Search%3AForums%3Alink%2F3.7.5
And since you mentioned Lightroom:
https://helpx.adobe.com/lightroom-classic/kb/supported-versions.html?x-product=Helpx%2F1.0.0&x-product-location=Search%3AForums%3Alink%2F3.7.5
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