Ok, suddenly I can cast spells without using magica. This occured for the first time on the courtyard of the College, so I assumed it had something to do with the magic focal points there. But now I'm standing near Saarthal, and I can still cast spells without depleting magica. While this is pretty useful, and I defeated the entire College with my newfound power, it kinda messes up my experience, so I'd like some advise how to fix
this.

Are you wearing any special armour?
Look at your active effects and see if there is anything weird

Are you wearing those special gloves?

I bet you were cleaning the focal points for Drevis Deloren. Enjoy it while it lasts. It doesn't last long.

No gloves, however, I have some fortfiy magica effects(2x +100, 1x+25) that I can't explain.

What Abacus said. It happens after you clear the focal points and will go away sooner or later

Ok, that explains it. I cleaned the focal points, so that would be the reason then.

You most likely did the focus point quest. It gives you incredible magicka regen for an hour or so. Use this opportunity to train your skills.

Yes, you have to wait for a long time for this effect to disappear. It doesn't seem to dissipate from waiting or sleeping, and if you are playing with an adjusted timescale, it can take a ridiculous amount of time.

I had the same problem and found it to be extremely annoying, almost like playing in god mode. As I'm playing with reduced timescale, the only way I was able to get rid of this effect was by fast traveling about 10 times to different locations. Keep fast traveling and eventually it will disappear.