[2021] 3.0.3 Slow save / freeze at save

Does this only affect this one particular galaxy?

Do you get anything like this if no mods are involved?  

We can only help with unmodded games here I'm afraid. For help with mod issues please check with the modding experts here:

Stellaris: User Mods

All things related to mods. Ask questions, post your own mods, get inspiration! forum.paradoxplaza.com  

I'm not aware of any extra diagnostic or debug options or flags with this game, I'm afraid.

But if there were, they wouldn't be recording stuff like slow file system or online access, that's really in the realm of Windows. Have you looked at the performance graphs in task manager?