One possibility of having a planet with with an orital period of 365 Earth years, would be to have the planet orbit around a group of stars instead of a single star.
Assume that two stars orbit each other in an almost circular orbit with a semi-major axis of five million killometers.
Suppose the system has another very similar pair of stars with a similar orbit around each other. The two pairs might orbit each other with a semi major axis of twenty five million kilometers.
And then suppose that there are two such systems of four stars orbiting each other with a spearation of about one hundred twenty five million kilometers.
If there was a system with eight stars orbiting their common centers of gravity within about one hundred twenty five million kilometers of the common center center of gravity, a planet could orbit around the common center of gravity of the entire system with a stable orbit if it was far enough beyond the orbits of the stars.
It could probably have a stable orbit with a semi-major axis of six hundred and twenty five million kilometers five times wider than the separation between sets of stars.
It might be able to orbit with a stable orbit even closer to the stars.
For a circumbinary planet, orbital stability is guaranteed only if the planet's distance from the stars is significantly greater than star-to-star distance.
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.[9]
https://en.wikipedia.org/wiki/Habitability_of_binary_star_systems
Two to four times one hundred twenty five million kilometers would be two hundred fifty billion to five hundred million kilometers.
And of course stable orbits would be possible out to distances of tens or hundreds of billions of kilometers, so there would be a wide range of orital distances possible.
So if you assume that all the eight stars have very similar masses and luminosities, you can choose a mass and calculate an orbital distance where the planet has an orbital period of 365 Earth years with that total mass of the eight stars.
And you can choose a mass and thus luminosity for the stars and then choose an orbital distance where the star receives enough radiation from the combined eight stars to have the proper surface tempertures.
But the problem would be combining the right orbital period and the right amount of radiation. Choosing a combined mass and luminosity of the eight stars so that the planet has an orbital period 365 Earth years long and also receives the right amount of radiation for the right temperurature might be impossible.
But replacing a central star with a group of two, three, four... and maybe up to eight central stars, may make the problem more flexible than using only one star.
Fortunately, I have thought of a diferent type of year a planet could have. I will add that to my answer later.