Here is my issue with the client:

1. I have bough new DLC Rum Pack in client
2. However this new DLC is missing from the list of available dlc in game page
3. I went to GOG web manually downloaded from web and installed
4. Next Galaxy Client lost all previsous DLCs (previous 4) and verify command for the game is showing "NOT AUTHORIZED" result.

Is this normal behavior of this client ?
Is it possible to fix it?

Had to do your listed steps 1 to 3 myself before in order to get the Rum Runner's Pack working - so that is (for now) the norm I assume.

However, nothing within the client changed for me. I still see that i own 3/3 DLC and - I checked - have no problems verifying my files. Restarting the client/computer didn't do the trick?

That's interesting. I too couldn't install the new Rum DLC with the GOG Galaxy Client. That's why I too downloaded the DLC manually on the website. After installing this, the client still listed the DLC as missing, so I thought I'd simply do a verify on my installation. This lead to a loop, every single time I selected Pillars II in the client, the client would just do a verify AGAIN. I tried a couple of things, but ultimately I had to uninstall the client...

After I installed it again, it wasn't trying to verify my installation anymore in an infinite loop, but the DLC is still "missing" from the client's viewpoint. It's working ingame of course... Never had such problems with Galaxy before.

I've had that verify loop with both Pillars of Eternity 2 (after the 1.02 patch) and BattleTech (after the 1.04 patch) as well. I deleted "C:\ProgramData\GOG.com\Galaxy\storage" and re-imported my game library which seemed to fix it. Not sure what's going on with this latest version, I never had that problem on my other PC after updating either game so i'm not sure what's triggering it.

Do you think that fix would work when I am having the same problem and I can't actually even touch basically any options. Galaxy doesn't recognize the version I have.

Yeah it should work, but be warned if you have any games using a beta branch it might not re-import them properly.

Close Galaxy first, delete the storage folder, restart Galaxy (your game list should be empty), then use the "Scan and import folders" option to re-import your games. Depending on how many games you have installed it might take a long time, just let it finish before doing anything.

You can keep the folder you deleted in the recycle bin and restore it in case it doesn't help or causes another problem. Just make sure you always close Galaxy before deleting or restoring that folder.

These issues are quite frustrating.

I had the same problem as the OP and ended up downloading and installing the Rum Runners Pack manually. This solved the issue in that the content appears in-game now (the most important part) but the Galaxy Client no longer shows any DLC in Deadfire's Settings page, where before the 8 pre-Rum Runners DLC were listed there, nor does it say "X DLC" (where X would be the number of installed DLC) next to the game's version number, where before it said "8 DLC"

When I start the game and open the overlay however, it does say "9 DLC" next to the version number. *shrug* It would be nice to know whether this is a Deadfire issue or a Galaxy issue, and whether it will be fixed soon.

It is a Galaxy issue and here is a workaround for it:

https://www.gog.com/forum/pillars_of_eternity_series/rum_runners_package/post8