It is impossible to have an oval habitable zone around a single star.
If there are two stars, they could have two separate habitable zones separated by space. In that case any habitable planet would have to orbit around only one of the stars in only one of the habitable zones. That is called an S-type orbit.
Or the two stars could be close enough that their two habitable zones overlapped a little or a lot.
If the habitable zones of the two stars overlapped a lot, a planet orbiting around both of the stars in a P-type or circumbinary orbit could be within the combined habitable zone of both.
For a planet in a P-type or circumbinary orbit to have a stable orbit it's distance from the center of gravity of the two stars should be at least 2 to 4 times the separation between the two stars.
The minimum stable star-to-circumbinary-planet separation is about 2–4 times the binary star separation, or orbital period about 3–8 times the binary period. The innermost planets in all the Kepler circumbinary systems have been found orbiting close to this radius. The planets have semi-major axes that lie between 1.09 and 1.46 times this critical radius. The reason could be that migration might become inefficient near the critical radius, leaving planets just outside this radius.
So the farther away a habitable planet is from the two stars, compared to the separation between them, the wider the circumstellar habitable zones of the two stars will be, compared to the separation between them.
So the combined habitable zone of the two stars can not be very oval, or the planet as it orbits would sometimes be outside of it.
Note that the quote says that if the minimum stable orbit of a circumbinary planet is 2 to 4 times the separation between the two stars, the minimum orbital period of the circumbinary planet will be 3 to 8 times as long as the orbital period of the stars around their center of gravity.
So since the planet will take longer to orbit the 2 stars than the two stars will take to orbit each other, the relative orientations of the two stars and the planet will change.
Sometimes the planet will be on the line between star A and star B, beyond star B. As star B orbits faster than the planet, it will move ahead of the planet. Eventually the line between star A and star B will be at a right angle to the line between their center of gravity and the planet.
As star A orbits faster than the planet, it will catch up to the planet, and eventually star B, star A, and the planet will be in a straight line, with the planet beyond star A.
So if the habitable zone is very oval, it will move faster than the planet, and sometimes move so far ahead that the planet will be outside of it.
The habitable planet can never have a orbit where it moves at the same speed as the outer point of the combined habitable zone of the two stars. And it would greatly reduce the habitability of the planet if it was sometimes outside the habitable zone.
So there is a considerable limit to how oval the combined habitable zone can be, even if the planet has a perfectly circular orbit. And if the planet has a more eccentric elliptical the habitable zone, moving relative to the planet, will have to be less oval so that the planet will never be outside of the habitable zone.
So while the combined habitable zone of two stars could be slightly or very oval in shape, depending on their separation, no planet in an P-type or circumbinary orbit, whether circular or elliptical, could stay within the moving combined habitable zone all the time if the zone was very oval.
So you might as well go with a single star with a perfectly circular habitable zone, and make the planet have an eccentric elliptical orbit that stays within the habitable zone, and so is reasonably but not highly eccentric.
And of course you could have a planet with an orbit that takes either closer to the star, or farther from the star, or maybe both, than the habitable zone, giving it short periods of intense heat or intense cold, or both. That could work if the planet spends most of its orbit and time within the habitable so its temperatures are mostly endurable for most of the orbit.
My comment at: https://moviechat.org/tt0058824/Lost-in-Space/58c7261d5ec57f0478eea649/The-orbit-of-Plrplanus is an attempt to explain how a planet with a highly eccentric orbit might possibly, repeat possibly, have comfortable temperatures most of the time.