Part One: A Multiple star.
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 million 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.
Added 11-19-2022.
Part Two: Tidal heating of an exomoon.
Suppose that the world in the story is a giant moon, large enough to be habitable, orbiting a giant planet, or maybe a brown dwarf, which in turn orbits around the star (or stars) in the system.
So the giant planet with the habitable moon could orbit the star at the corret distance to give it an orbital period of 365 Earth years based on the mass of the star (or stars).
But if the central star has a low enough mass to shine fairly steadily for billions of years in order for the planet to become habitable for oxygen breathers, the planet and the moon would have orbit out where the radiation from the star would be very faint and insufficient to make the planet warm enough for liquid water using life.
If only there was some other potential sources of heat for a giant moon orbiting a giant planet.
Tidal interactions between the moon and its planet can cause sufficient tidal heating for liquid water oceans on the surface.
Theoretical studies of the possibiity of habitable exomoons of giant exoplanets show that the extent of tidal heating on those exomoons depends on their distance from their planets, among other factors. As a rule the closer to the planet, the greater the tidal heating on the moon.
If the moon orbits too close to the planet, the tidal heating will be enough to initate a runaway greenhouse effect, turning all the surface water into atmospheric water vapor. If the moon orbits even closer, the tidal heating will cause excesse vulcanism on the moon, making it a volcanic hell like Io.
Thus the phrase "habitable edge" for the inner limit of how close a moon can orbit to its planet while avoiding excessive tidal heating.
And it should be obvious that if the planet and moon orbit too far from their star for stellar radiation alone to warm the moon enough for liquid water, the moon could still be warm enough if it orbits outside the tidal edge but close enough for enough tidal heating for liquid water oceans.
There would still be a problem with the moon getting enough light from the star for photosynthisis on the surface of the moon for plants to produce an oxygen atmosphere.
Fortunately, a small increase in the mass of a star will cause a greater increase in the luminosity of the star. Thus the correct distance to receive a specific amount of radiation from the star will increase more than the star's mass and graitational pull on a planet. So the more massive and luminous the star is, the longer the orbital period of a planet receiving exactly as much radiation from the star as the Earth will be.
Using the most massive and short lived star that I dare to, the more massive end of spectral class F stars, I found that a planet at the Earth Equivalent Distance from such a star would have an orbital period several Earth years long. I also found that putting two stars at the center of the star system would inrease Earth Equivalent distance, but it would increase the combined stellar gravity more and would make the orbital period at the Equivalent Distance shorter than for a single star of that mass.
And of course you would want a planet in an orbit so far that it would have a year 365 Earth years long, so it's orbit would be several times as far from the star as an Earth Equivalent Distance would be anyway. But that might possibly help with giveing the habitable moon enough light for photosynthesis.
With years 365 Earth years long, the astronomical seasons would each be 91.25 Earth years long. And some of the comments express fear that such long hot summers and long cold winters would be deadly for life on the planet, or in this case, exomoon.
The way to handle this is to give the planet an a vert low axtial tilt, so that the inclination of incomming solar rays is almost exactly the same in every season of the year.
And in the case of a giant habitable exomoon orbiting around a giant planet and getting most of its heat from tidal heating, the astronomical seasons wuld not cause climataollgical seasons on the Moon. The temperatures would be quite constant all year.
So why would the people on a planet or moon with such even and unnoticable seasons brother with counting orbital periods around the star and making them the years that their calendars are based on?
Because of the changing night time stars. At any given moment one side of a planet or a planet's moon will be facing toward the star of the system, and the atmosphere on sthat will scatter the bright star light and making the sky appear opaque and hide the stars. And on the opposite side of the planet from the star, the atmosphere will have light from it to scatter, and the sky will be transparent, and the stars will be seeen. The stars which are in the opposite direction to the star in that system.
On Earth, as the Earth slowly orbits the Sun, the direction opposite to the
slowly changes, and so the stars which are visible at night slowly change over the year.
And so the stars visible at night on that planet will slowly change over the course of a 365 Earth year orbit. So posssibly the stargazers on that planet treasure star charts handed down from earthly decades and centuries earlier during the 365 year long orbit and calculate how long wit will be until eachs uch set of stars is visible again.
So that might give the natives of he planet a reason to have a calendar period equal to 365 Earth years, or one orbital period of the planet, even without dramatic seasons.