The issues with the compression fitting have been addressed.
The brass flange fitting, the rubber gasket, and the threaded pipe is the "toilet spud". Replacements are available if the rubber is perished or the metal parts somehow damaged.
The flange nut looks pretty well bonded to the threaded portion. Soak well with WD-40 and let it soak in. There are splines inside the spud on which one would apply an internal spud wrench to keep the threaded pipe part from turning. You may find some other chunk of metal that will wedge against the splines, which in turn can be held by a conventional wrench. Holding the spud in place, remove the flange nut with a suitable tool.
Once the flange nut is removed, push the threaded pipe part inwards, but ensure it will not fall into the toilet. The part inside the toilet is conical shaped. Pushing it inwards will give enough free play that the rubber gasket can be pulled out. Once the rubber is out, there will be enough clearance in the toilet hole that the threaded pipe part can now be removed.
Examine the parts and evaluate if replacement is necessary. If the rubber is not too far gone, it may be possible to clean it, treat it with some sort of rubber treatment, and reinstall. If the rubber is cracked, hardened, rotted, or brittle, it will need to be replaced. The nut should be tightened firmly enough to ensure the rubber seals well against the toilet, but not so tight the rubber gets pushed out of position or the toilet gets cracked or broken.
Nothing has changed, your toilet still drains too slowly, you still need to clear the obstruction. The bowl completely clearing will sometimes happen with partially obstructed toilets because, due to the very restricted passage, the vent air that normally breaks the siphon action cannot make its way to the bowl until long after all the tank water has been completely drained into the bowl, leaving no fresh water to refill the bowl.
As soon as the passage is cleared to its normal size, the vent air will have room to work towards the bowl and quickly break the siphon. The bowl is then refilled with the remaining fresh water, ready for another flush cycle.
ADDENDUM
Depending on the nature of the obstruction, if it's difficult to completely clear with an auger, and assuming the toilet bolts are not too badly corroded, it's worth removing the toilet and working at the obstruction from both ends. It's usually easier than most people think. There is still a portion of the passage that is difficult to reach, but you've doubled your chances. For the typical floor mounted residential toilet you will at least need a fresh wax ring to reinstall the toilet.
Best Answer
If you had "the sewage line get backed up" all along and didn't do anything to fix it (replacing the water line doesn't) then the sewage line will only get worse.
As for your tub (I think you want me to guess you shower in the tub instead of having both a tub and a separate shower), it probably connects to the sewage line after the clog that affects your toilet.