I went through the same path as you - I think I even landed up with 14 takeout files as well!

Its a bit of a trial, but quite doable. Its likely that things have improved since I did it about 6 months ago.

*Getting the files from takeout* I tried downloading the files onto my laptop via a browser, and then copying them over to my NAS, but quickly gave up. The best approach is to download them directly to the NAS. As you pointed out auth/cookies is an issue. There are multiple ways of solving the issue, but for me I found the best way was to use chromes dev console network view to identify the network request for each file, then right click on it and select "Copy cURL". SSH into my nas and use that command to download the file. There is a bit more info on how to do this here:

https://trog.qgl.org/20241001/downloading-a-google-takeout-f...

*Importing them into immich*

Once I had all my takeout files on the nas, I used immich-go to import them: https://github.com/simulot/immich-go

This took a bit of tweaking to get the right set of command line args that worked well for what I wanted it to do. I also found immich errored out a few times during the import. Fortunately immich-go can just pick up the import where it left of, so I kept re-running it until everything was imported.

*Cleaning it all up* If you just want a huge flat dump of your files your probably good. In my case there were various things I wasn't quite happy about. The default handling of stacking edited images with the originals in albums wasn't what I was after. I wanted to replicate sharing of albums with immich users to match what I had in google photos. For all this kind of cleanup work, I found it quite helpful to work with an AI agent. Give it an API key for your server + the url and get it to help you write cleanup scripts.