Electrical – have two blue and two red wires in the ceiling light fixture

The cable on the left runs to the switch. Power comes in from one of the two other cables via red, runs down the red of the switch cable to the switch. When the switch is closed, power runs back along the black and into the light via the brown. Goes thru the lamp into the blue, which connects to the common neutral black of the other two cables.

Switch legs can be confusing because the neutral coloured wire carries power back the the switched fixture. All is as it should be though.

It looks like a standard "power on the end, lamp in the middle" 3-way arrangement. However (for whatever reason) they chose to make the travelers black and white on both segments.

Travelers can be quite a dog's breakfast, I've seen 3-way circuits where the travelers change colors on every segment. Choosing the same colors thru makes some sense -- however white should not be one of the chosen colors. though the far, far better way is to pick a colored tape color such as yellow, and mark both travelers yellow (they are interchangeable, they can be the same color).

That's because white is special in Code rules. Colored wires (hots) cannot be remarked to be neutral. But white wires can be remarked to be a hot wire. The last guy should've made red and black the travelers and tagged white with colored tape in the segment where it served as switched-hot. That would've been reasonable.